E. O. Wilson vs. math (UPDATEDx16 & corrected; no further updates)

Via Tim Poisot, I see that E. O. Wilson has taken to the pages of the Wall Street Journal to explain why “great scientists don’t need math” (that’s the title of the piece). (correction: As pointed out by a commenter, that’s the title on the tab at the top of the web page; the headline on the piece is “Great scientist ≠ good at math”)

Like everyone, I have huge respect for E. O. Wilson. He’s a great scientist and then some–if you cut him in half, you’d have two great scientists. But this piece isn’t one of his better efforts. Indeed, I think it’s really poor. It’s basically Wilson overgeneralizing from his own example, and indeed I think actually misdescribing his own example. And the piece has the potential to do some damage (at least, as much as any single editorial ever can, which may not be all that much), because of Wilson’s prominence, the prominence of the venue, and because it includes advice for students. Really bad advice. So I’m going to push back, hard.

Wilson claims that strong math skills are relevant only a few disciplines, like physics. Elsewhere, great science is a matter of “conjuring images and processes by intuition”. He goes on to say that discoveries arise from disciplined daydreaming, from writing field notes, struggling to explain something to a friend, or eating lunch alone. And that making important discoveries requires “hard work and focus.”

I’m sure Wilson is describing his own approach here, and it’s worked for him. But I have to say, it’s surprising to find someone as famous for his breadth of knowledge as E. O. Wilson generalizing so unthinkingly from his own example. I wonder what his late collaborator Robert MacArthur would think of the notion that intuition alone is enough. I wonder what Bill Hamilton would think. Or R. A. Fisher. Or J. B. S. Haldane. Or Robert May. Or John Maynard Smith. Or George Price. Or Peter Chesson. Or Dave Tilman. Or lots of other great ecologists and evolutionary biologists I could name off the top of my head. Would Wilson seriously argue that none of those people were great scientists, or that they never made any great discoveries, or that the great discoveries they made arose from intuition unaided by mathematics? And as for the implication that theoreticians don’t daydream, don’t ever struggle to explain things to friends, don’t eat lunch alone (?!), don’t work hard, and don’t focus, the less said, the better (and if that’s not the intended implication, what is the point of this passage?)

Wilson does go on to say that following up the initial intuition often requires technical mathematical skill, and that’s where collaborators come in. But he makes clear that he sees this as a purely technical exercise. The important part, the creative part, is already done before the mathematical collaborator is brought in. Indeed, he emphasizes how easy it is for empiricists to find mathematical and statistical collaborators, compared to how hard it is for mathematicians and statisticians to find scientists able to make use of their equations.

Again, I wonder what Robert MacArthur, or indeed any mathematician or statistician, would think of the notion that collaboration with an empiricist is a routine and purely technical exercise. Or of the notion that good mathematical collaborators are a dime a dozen.

Having said that, I certainly agree that theoreticians often find it hard to find empiricists who will make use of their equations. But whose fault is that? Seems to me that the fault often lies with empiricists who stick with their intuitions come hell or high water, and who actively resist the discipline that mathematics imposes on their groundless daydreaming. Intuition is great–as long as it’s only a starting point, and as long as you’re prepared to give it up when it’s proven wrong, even if there’s no better intuition to replace it with. Unfortunately, that’s really hard to do.

Wilson goes on to say that “possibly no more than 10%” of theoretical studies in biology have any lasting value. I’m happy to agree–in fact, I bet it’s lower. But it’s just as low for empirical studies. The vast majority of all studies in science are of little lasting value, since the vast majority not only don’t report any major new discoveries, they’re hardly read or cited. Wilson thinks he’s arguing for the irrelevance of much theoretical biology here, but he’s actually arguing for the irrelevance of pretty much all everyday science not reporting a major breakthrough.

Wilson says that theory is only useful when it describes the actual world. To be useful, theory has to concern “the possible permutations that actually exist on earth”.

You cannot be serious! Indeed, this is so obviously wrong that I’m sincerely mystified how someone as sharp as E. O. Wilson could possibly say this. The claim that only descriptions of our actual world are useful, everything else being an irrelevant hypothetical, will come as news not only to every theoretician, but to every empiricist who’s ever conducted a manipulative experiment. I mean, come on! Does E. O. Wilson really need a snarky blogger like me to explain why experiments are useful? Does he really need me to explain that the way you learn why the world is the way it is, is by studying how it isn’t? Does he really need me to point out that the way you learn how the world works is by manipulating it so that it works differently than how it actually does? Because that’s what an experiment does–it creates unrealistic conditions, conditions that quite literally would not have occurred if not for the intervention of the experimenter. That’s the whole point of experiments. And it’s the whole point of piles of mathematical models too. When Fisher famously asked “Why does most every sexual species only have two sexes?”, he answered that question by modeling species with three or more sexes, a condition never observed in nature. When Fisher asked “Why is the sex ratio usually 1:1?”, he answered that question by modeling what would happen if it wasn’t 1:1. And so on–I could keep giving examples like this all day. But E. O. Wilson can’t possibly be unaware of this–so why did he write as if he is?

Wilson goes on to advise students that, while they ought to learn more math if their “competence is low”, they can “do outstanding scientific work” with they math they have, so long as they’re careful to avoid specializing in fields requiring “close alternation of experiment and quantitative analysis”, such as “most of physics and chemistry, as well as a few specialties in molecular biology”. It’s totally unclear why students should bother learning more math if they can do “outstanding scientific work” without learning more math, but leave that aside. To students reading this who rightly admire E. O. Wilson and so might be tempted to take his advice here seriously: he has just given you terrible advice. Every field of biology requires “close alternation of experiment and quantitative analysis”. This has been true for decades. I have no idea what E. O. Wilson is talking about here. Seriously: you are not going to make any major discoveries in any field of biology if you don’t know mathematics or statistics, and don’t plan on conducting experiments or quantitative analyses! And Wilson’s claim that deep interest in a subject, combined with deep immersion in masses of data, is sufficient, because hey, it worked for Charles Darwin, is utter rubbish. First of all, just because it worked for Darwin (or Wilson) doesn’t mean it will work for you, and just because it worked in the 19th century doesn’t mean it will work in the 21st. If for no other reason than that there are plenty of people out there, in every field, who not only have a deep interest in the subject and an encyclopedic knowledge of the data, but who know a lot of mathematics and statistics. Second of all, the notion that Darwin got his ideas by just compiling masses of observational data and then thinking hard about it is just false. Darwin read very widely, including outside of his field. The idea for evolution by natural selection was inspired in large part by his reading of an economist, Thomas Malthus. Darwin also considered the relevance of lines of evidence from fields as distinct (even in his own time) as geology, embryology, and animal husbandry. And he spent the last 40 years of his life running experiments (and if statistics had existed back then, he’d surely have used it to help him design and analyze his experiments).

Wilson concludes with what he calls “Wilson’s Principle No. 2: For every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.” This is question-begging, because it doesn’t specify when a scientist’s “level of mathematical competence” is determined (is high school mathematics enough? How about just middle school mathematics?) And it’s false.

Wilson says he’s dismayed by talented undergraduates turning away from science because they don’t know math. I’m dismayed by a professor catering to their math phobia rather than trying to overcome it. Make them do the math! Someday, they’ll thank you for it.

UPDATE: Tim Poisot’s own thoughts are here. And the Math-Frolic blog weighs in.

UPDATE #2: This post seems to have won the intertubes. There are now discussions going on on Reddit (here and here) and Metafilter.  Wide range of views, of my post and Wilson’s original piece. The strongest defenses of Wilson basically take the line Terry McGlynn and others take in the comments here: Wilson’s piece was autobiographical, and it’s unfair (or at least uncharitable) for me to read it as making more general claims. My reply to this line is in the comments in response to Terry, and I won’t repeat it here. Also saw some other good comments, such as the point that there’s a difference between understanding math and being able to do it, or do it easily. It’s quite possible to get by in science, even these days, without being able to do much math (at least not without a textbook by your side), but much harder or impossible to be able to get by without understanding it. And the point that, for all of Wilson’s protests about how poor he is at math, that depends who you’re comparing him to. I think that’s a good point. In his autobiography, he notes that he’s been taught how to solve partial differential equations and been walked through the mathematics of quantum mechanics. He emphasizes that he quickly forgot how to solve PDEs and how quantum mechanics work. But you know what–I don’t know how to solve PDEs or how quantum mechanical math works, and never have! Wilson may have come to math late, and may not enjoy it, but he eventually did a reach a level of understanding and competence that I’d say is typical or even a bit higher than that of the average empirically-oriented ecologist or evolutionary biologist. And even if he’s not actually doing any math himself, I am sure that his understanding of it is broadly helpful to him, in particular in his interactions with his collaborators. And so while Wilson considers his own example inspirational to non-mathematical biology students, I can tell you, based on long experience teaching undergrads myself, that many of them would find even his level of mathematical competence intimidating! Even very sharp undergrads often feel this way. One of the very best students I’ve ever taught at Calgary, someone who is really good at the mathematical side of ecology (far better than I was as an undergrad) insists continually that not only doesn’t she like math, she isn’t good at it and never will be. I truly believe that Wilson’s piece, even read as pure autobiography, is not actually the way to help most of the students he’s trying to help.

UPDATE #3: Razib Khan of the Gene Expression blog over at Discovery Magazine weighs in with a great post. Lots of good context about Wilson (including the fact, noted by Terry in the comments here, that one reason many people (not me) are so upset with Wilson’s editorial is that he recently put his name on a very controversial and heavily-mathematical Nature paper on the evolution of eusociality despite almost certainly not understanding the math). Also good stuff about other great biologists who likely would take a different view of the role of mathematics in biology. For instance, did you know that Bill Hamilton was self-taught in mathematical population genetics, and that formally-trained theorists initially were very skeptical of his models?

UPDATE #4: And over at Psychology Today, Jonathan Wai shares his research on the mathematical abilities of scientists working in different disciplines, as compared to the general population, and as compared to verbal and spatial abilities. In some ways the results aren’t surprising (biologists are, on average, far more able at mathematics than the average person, though not as able as physicists or engineers). But it reinforces the point that, while some biologists certainly are more mathematical than others, it is not true that you can succeed in biology these days no matter what your mathematical ability, if only you find the right subfield. Wai also notes that, on the evidence of his own eloquent writings and self-descriptions, Wilson himself is probably more skilled verbally and spatially than mathematically. Wai makes the interesting suggestion that Wilson himself may be mixing up evaluation of his own mathematical abilities relative to his own abilities in other areas with evaluation of his own mathematical abilities relative to those of other biologists, or of students. I think this is an important general point (whether it’s correct in Wilson’s specific case, I don’t know). I suspect it’s part of what’s going on with the very sharp undergraduate of mine I mentioned in a previous update. Relative to other students, she’s extremely good at math. But math feels harder to her than other subjects do, and she enjoys it less. Which may be part of what leads her to feel (incorrectly!) that’s she’s not good at math as judged by some standard external to herself.

UPDATE #5: Graduate student Manu Saunders of Ecology Is Not A Dirty Word weighs in, defending Wilson’s point of view. It’s a good piece, though I don’t agree with all of it. I think that, like Wilson and many other empirically-oriented ecologists, she has too limited a view of the ways in which mathematics can help us learn about nature. Manu, if you’re reading this, I highly recommend Bill Wimsatt’s great old piece on false models and how they’re often empirically useful precisely because they’re false. 😉 And Terry McGlynn of Small Pond Science has followed up his comments here with his own post. Terry’s an ant guy who I believe has met E. O. Wilson, and knows Wilson’s work much better than I do. So he read Wilson’s piece with rather different eyes than I did (though not necessarily approving eyes). Terry’s post starts out by talking at length about intellectual “tribes” in science, the benefits and costs of joining one (and the difficulty of avoiding joining one), and about interactions within and between tribes. He notes, correctly in my view, that E. O. Wilson himself recently helped start a big, unproductive intertribal battle over the evolution of eusociality. He goes on to suggest that Wilson’s piece in the Wall Street Journal was at least in part calculated to start similar intertribal war between empiricists and theoreticians. And that in reacting as I did, I basically gave Wilson what he wanted–a predictable, boring fight between artificial camps (artificial because hardly anybody, certainly not Wilson and certainly not me, is purely theoretical or purely empirical). He goes on to talk about what he sees as the real issues here, the ones that members of both tribes ought to be able to discuss productively (not agree on how to resolve, discuss productively). Go read the whole thing, it’s long, but it’s well worth your time. And then you can come back here and check out some old posts I’ve done on why theoreticians and empiricists often talk past one another, and some theoreticians’ eloquent attempts to explain themselves to empiricists.

UPDATE #6: And now Paul Krugman (!) weighs in. He uses Wilson’s piece (which he mostly likes) as a jumping off point to talk about something he often emphasizes, the way he uses simple models (“simple” by the standards of modern economics research) to undermine our pre-mathematical intuitions about economics. He also notes that what’s worked for him won’t work for everyone, and that everyone thinks the optimal amount of math to know is “exactly the amount you personally happen to know”. The big differences between Krugman’s reaction, mine, and Terry’s are a nice illustration of how people’s reactions to any piece of writing are shaped by their own experiences and knowledge. Krugman, like Wilson, has always been keenly aware of his own limited math skills relative to the most mathematically-oriented people working in his field. And so he’s inclined to like Wilson’s piece, with the caveat that he does see simple math as being hugely important and thinks you’ll avoid serious mistakes if you know some basic math. I read Wilson’s piece as an ecologist, who has worked hard to purge the field of widespread, serious mistakes arising from failure of too many ecologists to understand even very simple mathematical models. I also read Wilson’s piece in light of other recent pieces from prominent senior ecologists, lamenting that ecology is losing its natural history roots in favor of mathematics. And I read it as an instructor who works very hard to help math-phobic biology students appreciate how math can help them do biology better, and convince them that they can get it. Terry reads Wilson’s piece as someone who’s read a lot of Wilson’s stuff, has met Wilson briefly, and who’s talked to a lot of people who know Wilson well. Which causes him to read Wilson’s piece as deliberate bomb tossing, an intentional provocation to theoreticians. None of which is to say that any of us is totally right, or totally wrong. All of our readings have objective support in Wilson’s text itself, but the text itself isn’t sufficient to narrow the range of defensible readings down to a single one.

UPDATE #7: And from beyond the grave, JBS Haldane disagrees with Wilson!


HT to Terry McGlynn for injecting a bit of levity into the discussion by pointing this out. 😉

UPDATE #8: Jag Bhalla weighs in with a guest post at Scientific American, and he’s been kind enough to link to us and to Terry over at Small Pond Science. Jag offers some historical perspective, tracing back to Galileo’s faith that “the Book of Nature is written in the language of mathematics.” He pushes back against this faith, arguing that the sort of math physicists use has permeated all fields, to the detriment of those fields because that sort of mathematics isn’t good at dealing with stochasticity, and conditionality. I enjoyed Jag’s post, though I found it a bit too vague and sweeping (maybe because the argument he’s trying to make is too big to be easily compressed into blog length). There are huge areas of math (and programming) for thinking about (and simulating) highly complex, stochastic, nonlinear, non-equilibrium systems with many players behaving in their own unique ways, and those are precisely the sorts of systems that are hardest to think about without the aid of mathematics. And conversely, as Paul Krugman (linked to in an earlier update) notes, even highly complex, stochastic, systems with many players behaving in complex ways often can be partially understood in aggregate via very simple mathematics, in ways that demonstrably improve over the verbal narratives for which Jag argues. At the moment, a very strong case can be made that massive damage is being done to the global economy, and to the lives of many millions of people, on the basis of verbal narratives about how economics works. Narratives that are both intuitively appealing, and false. So while I actually agree with Jag that there are indeed huge, important chunks of the social world we currently can’t (and quite possibly never will) be able to fully describe with mathematics in a sensible way, his post can be read as an argument for different sorts of math, rather than as an argument for the limits of math.

UPDATE #9: Homologous weighs in, coming down broadly on Wilson’s side on the grounds that overreliance on mathematical models in finance and other areas has led people badly astray. And Larry Bartels of political science blog The Monkey Cage chimes in, agreeing with Krugman’s point of view. Larry’s work used to be more mathematical, but he found that “sophisticated” math was subtracting more than it was adding. Theory based on fancy math often makes only qualitative predictions that are hard to test. He finds that basic mathematical intuition and statistical estimation techniques, focused on magnitudes of effects, are actually more valuable for quantitative analysis of real data.

UPDATE #10: If you think I was hard on E. O. Wilson, you should read this take from West Hunter (a collaborative blog between an anthropologist and a physicist). Includes a famous line from Darwin which I can’t believe I’d forgotten about, and which I haven’t seen anybody else quote until now:

I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics;  for men thus endowed seem to have an extra sense.

Which gets back to a point many commenters have made: it’s true (though probably much less true than it used to be) that one can do significant scientific research while knowing less math than many other scientists do. But it’s also true that one can do better research than one otherwise could’ve done by knowing more math. Yes, we want to encourage math-phobic students to go on in science. But surely we want to encourage them to become as good at science as they can be–which means helping them understand and value math, not encouraging them to avoid it.

UPDATE #11: Writing at Slate, mathematician Edward Frenkel says that Wilson is wrong. His take is very much in line with mine, arguing that Wilson is overgeneralizing from his own example. Wilson could’ve said “I’ve been fine without much math, I have other strengths and I’ve been fortunate enough to have wonderful collaborators. But you don’t have to be like me, and indeed it’s not clear that you’d want to be in this day and age, so let me help you overcome your fear of math.” But he didn’t.

UPDATE #12: Theoretical ecologist Will Wilson has drafted an op-ed in response to E. O. Wilson’s (no relation) and put it up on Ecolog-L. It’s a very nice piece. Will takes the same autobiographical approach E. O. Wilson took. He talks about how he came to biology via physics, because he didn’t like all the memorization in biology, and about how mathematical biologists are just as curious and question-obsessed as other scientists (echoes of Fisher here). A nice reminder that students get scared away from biology for more than one reason. Students start choosing their tribe very early, often without realizing they’re choosing a tribe, just because different students have different backgrounds and interests. I haven’t looked at the other related posts and comments on Ecolog-L (I tend to avoid Ecolog-L as a discussion forum), but there is discussion going on there if you want to check it out.

UPDATE #13: Financial blog (!) Above the Market weighs in. Emphasizes mathematics as a way to fight the many well-studied cognitive biases to which all of us (not just financial investors) are subject. And notes, correctly in my view, that Jag Bhalla’s “narratives” (see update #8) need not be seen as an alternative, non-mathematical way of understanding the world. Rather, by doing the math first, we’re often in a position to build better narratives, to tell ourselves true, unbiased stories. I’ve tried to do this myself, for instance using simple, intuitive analogies to convey mathematical results, thereby undermining the bad intuitions driving zombie ideas.

UPDATE #14: Over at the blog of the BEACON Center for the Study of Evolution in Action, grad student Luis Zaman says that “consultation ≠ collaboration”. He uses the interdisciplinary work that BEACON scientists do as an example of what truly collaborative work at the interface of mathematics, biology, and computer science looks like. It’s not a matter of biologists just roping in mathematicians when they need to formalize their intuitive ideas.

UPDATE #15: Brand-new ecology blogger Jennifer Wright has chosen the Wilson debate as the subject of her very first post. She relates her own struggles with math, and argues that we shouldn’t try to “force feed” math to students who struggle with it.

UPDATE #16: Ok, I’m drawing a line under this. But not before linking to one more reaction to Wilson, from Mike the Mad Biologist. He juxtaposes a sober version of his reaction:

Of course, scientists need think conceptually and broadly, and the overemphasis on models can be harmful (economists are the worst about this, where they attempt to convince politicians to change reality when reality violates the assumptions of their models). But in an era of declining funding, having a well developed set of technical skills can keep you gainfully employed as a scientist

with an entertainingly less-sober version:

BREAKING!! Senior tenured faculty member at Harvard and leader in his field can find others to do the technical bits while he thinks Huge Fucking Thoughts. Guess what role you’ll play?

Good to have someone on the internet who makes me look like the restrained, balanced voice of reason. 😉

Changed my mind: let’s give the final word to Joan Strassman of Sociobiology (now there’s a good title for a blog if you’re going to post about E. O. Wilson!) A generous, balanced take on what Wilson gets right, and the many things he gets wrong. Also emphasizes a point not made sufficiently often elsewhere: “math” is actually all sorts of stuff, used for all sorts of purposes. Wilson unfortunately lumps together stuff as diverse as experiments, quantification, statistics, and mathematical theory of all sorts. This stuff does indeed all look the same to students brand new to it–it all involves numbers and symbols. But it’s surely our job as instructors to make clear what all these different sorts of “math” are for, when and why they’re useful, etc.

125 thoughts on “E. O. Wilson vs. math (UPDATEDx16 & corrected; no further updates)

  1. While I appreciate your post, I don’t share your great disappointment in Wilson’s article.

    The impression I got from Wilson’s piece was not that he was discouraging the use of mathematics. Instead, he was encouraging those with limited skills in mathematics to enter science/biology despite of there lack of skills (while, at the same time, trying to improve their skills).

    He wrote: “If your level of mathematical competence is low, plan to raise it, but meanwhile, know that you can do outstanding scientific work with what you have.” This is not an attack on mathematical or theoretical work, it is encouragement to those who might feel insecure about their own (lack of) abilities.

    I agree that skills in mathematics are immensely valuable and progress in ecology would not be where it is today without it. Nevertheless, we must accept it for what it is: just another tool in the ecologist’s tool set… not a barrier to entry as an ecologist!

    He clearly believes that there is a place for anyone in science when he writes: “For aspiring scientists, a key first step is to find a subject that interests them deeply and focus on it. In doing so, they should keep in mind Wilson’s Principle No. 2: For every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.”

    Not only do I agree with him, I think that scientist/ecologist/biologists should try to encourage a diverse group of people, skills, passions and talents.

    • Wilson may believe there’s a place for anyone in science. Doesn’t make it true. I agree that he’s trying to encourage a certain sort of student–but he’s trying to encourage them by pandering to the skills they lack, and by trying to inspire them with total unrealistic and unrepresentative examples like those of himself and Darwin. I teach dozens of students every year who start my classes nervous and unenthusiastic about the mathematical content. The vast majority say at the end that they’re glad they had to take my classes.

      Lack of math skills below a certain level is indeed a barrier to entry into ecology, or evolutionary biology. As well it should be.

      Encouraging a diversity of people with a diversity of skills, passions, and talents is great. But what Wilson is doing here is quite explicitly denigrating the value of mathematics, to the point that one can do without it entirely (’cause if you ever need it, you can find a technician collaborator to help you out). You do NOT encourage “a diversity of skills, passions, and talents” by explicitly saying that some skills, passions, and talents are far more important than others!

      • Point 1: I am not arguing that maths isn’t important. It is. If everyone had fantastic skills in mathematics then, yes, ecology would better and more effective.

        Point 2: I am arguing against the idea that you can only be a good ecologist if you have great skills in maths.

        Jeremy and Florian (and all those who commented later), you are both successful ecological researchers working on fundamental problems. I don’t doubt that your talents for mathematics were essential in your work. But you have to agree that not everything we call “ecology” is based on advancing theory and solving fundamental problems. My definition of “ecology” (not to mention “science”) is probably broader than yours because I consider the application of knowledge (engaging with policy makers, local stakeholders, conservation practitioners etc.) an important part of ecology too. I don’t think that people with these skills (but lacking maths talent) should be discouraged. Sure, they will not be publishing any papers in Ecology Letters, but that doesn’t mean that their contributions to ecology are of no value. On the other side of the coin, I don’t expect all fundamental ecology researchers to know the ins and outs of the Convention for Biological Diversity or the REDD+ programme, for example. Ecology needs a range of skills beyond those that one person can master; this is why we should encourage diversity. (So, like Jeremy ended, I don’t think we should raise some skills – including maths – above others)

        Point 3: As I said, maths skills ARE important, but they shouldn’t be a barrier to entry. Those who possess the skills shouldn’t exclude those without them. I feel that mathematical ecologists should strive to make their work more accessible (this is not he same as “dumbing it down”) not only because it might help the dissemination of their theories (http://www.pnas.org/content/early/2012/06/22/1205259109.abstract) but mainly because it will help break down this intimidating perception that you don’t have a future in ecology unless you are a maths whiz. This is particularly true in developing countries (I am from South Africa, btw) where the level of STEM education might not be as high as the levels you are probably accustomed to and many potential ecologists are “lost” because they are intimidated by (false) perceptions of what it is to be a scientist.

        Point 4: Despite the above, I do agree that we should all strive to improve our maths skills. I don’t think my opinions give anyone free pass to stop learning. Like you said Jeremy, we should all have skills “above a certain level”; but I think we disagree on what this level is.

        Endnote: I do realise that E.O. Wilson was talking about science in general and that I have dragged the debate into ecology and conservation biology. I realise that my descriptions of “stakeholder engagement” might not be considered as science/ecology. However, I don’t think my choice of definition changes my opinions, but I apologise in advance if I am guilty of setting up a straw man.

      • Re: point 2: With respect, you’re reading Wilson so charitably as to distort his meaning. He doesn’t say that you can get by without great math skills. He says, as a principle so important and general that he gives it a name and number, that no matter what your math skills, you can make major discoveries in most areas of biology, except for a few specific specialties in molecular biology. And while you may not be denigrating math, Wilson quite explicitly is. He says that premathematical intuitions and ideas are the important part, that the only value of math is for firming up and validating those intuitions, and that math that doesn’t describe the world as it actually is is valueless.

        Re: science being about more than making fundamental discoveries, I agree. But Wilson’s piece is about what you need to make major fundamental discoveries. You’re branching off into other issues. Which is fine, but please do recognize that you’re doing that. You’ve shifted from defending Wilson’s article to making entirely different claims.

        Re: math only being needed for fundamental work like the sort I do, sorry, but I’m afraid you’re incorrect. I doubt you’ll be taken seriously by policymakers, much less ever be in a position where you’re asked to give them advice, if you lack any mathematical or statistical expertise.

        Re: that PNAS piece about how theoreticians need to make their work more accessible, it’s wrong. Here’s the old post where I explained why. It’s mostly the fault of empiricists, not theoreticians, that empiricists mostly don’t read or understand theoretical papers or appreciate their value.

        If scientists from developing countries, or from any background different than mine, lack mathematical skills or find math especially intimidating, the solution to that is to train them appropriately. As I said in another comment, I teach dozens of undergraduate ecology majors every year who enter my classes frightened of math. At the end, they’re almost all glad that they were required to take the classes I teach, rather than having their untrained inclinations pandered to by being allowed to avoid quantitative material.

        p.s. I’ve had one math class since high school, although various other courses I’ve taken have had various sorts of quantitative material. When it comes to mathematical modeling, I’m entirely self-taught.

  2. I have to agree with Falco as to Wilson’s aim which is probably laudable, if perhaps somewhat misguided. I tend to think that the study of systematics is one of relatively few sciences where one can possibly get by without understanding too much math. Though even this descriptive field is moving toward molecular systematic tools. I’m not sure one can get far in ecological research or most realms of science without strong math skills. So much, if not most of science today consists of boiling things into numbers in search of statistical significance. I’m not sure this cult of statistical significance is all that good a thing. Though I had good math skills, this mathematical myopia certainly was one reason I did not choose to pursue science professionally.

      • I wouldn’t expect agreement and don’t get me wrong. I understand the power of statistics and that there is a very good argument for quantifying to a 95% certainty level against random chance. My problem lies in the way scientists communicate or actually how they don’t. Pick up a paper in a random journal and see how much of a primary research paper is in statisticese that a lay person would kill not to read because the meaning is absolutely and totally opaque to them. It is also how some scientists think and to some extent even how they talk. I fully understand that the lay are certainly not the intended audience and that paper space is limited and statisticese is highly efficient in word count terms. It often seems that the language and extreme level of scientific reductionism has limited the relevant audience of many papers to roughly five people on Earth. Ironically, when you delve deeply and follow citations backward (like a conversation) particularly in contentious areas or when feuds start, you realize that three of those five appear to hate the original author. Rant accomplished.

        I applaud your efforts and will say that the scientific blog is proving to be a remarkably refreshing counter to a long running trend of obfuscatory statistics in scientific writing. This is not a small thing! I think blogs are proving to be a great training ground for scientists in writing and communicating to a far broader audience. With globe fever raging, most people do not understand how much climate change is already locked in and just how unpleasant much of the Earth may become. Scientists more effectively communicating to a far broader audience may prove to be absolutely key to the survival of a good portion of the biodiversity of Earth and possibly the survival of our species as well.

        P.S. I don’t expect you or most scientists to agree with “obfuscatory statistics” any more than you did with ‘the cult of statistical significance’ or much in the rant portion of this post either. But I wanted to more fully explain my limited reasons for faulting this cult’s ascendance.

  3. Jeremy, I totally agree with you that this piece is a disservice particularly to young students in our field.

    Sadly, it seems to me that this opinion is not a singular “accident” by a great ecologist, but rather reflects a more general attitude in the community, at least in the older generation. Because, when Wilson says: “Many of the most successful scientists in the world today are mathematically no more than semiliterate.”, he probably does not refer to the Nobel price winners for physics but rather to his peers, the people he speaks to and works with.

    The reason for why that is so seems to warrant a sociological thesis, but I think it’s pretty clear that it is originates rather from the selection of people that go into ecology plus maybe the historical circumstances (no computers, no GIS, no sequencing) than from the potential utility of maths for ecological research. I see no reason why math (and statistics) should be less useful for an ecologist than for a physicist.

    I disagree with Falco that math is “just another tool in the ecologist’s tool set… not a barrier to entry as an ecologist!” and that we should “encourage a diverse group of people, skills, passions and talents” – it may be true that math was an optional skill at the time of naturalists, but if you look at the job market nowadays, my feeling is that at least 50% of all jobs ask for “strong quantitative skills” – a small part of these jobs may be explained by “statistical machismo” or mathematical mumbo jumbo, but by and large I would say the long-hanging fruit have been picked and ecology progresses to the analysis of larger and more complex datasets and theories that require a certain level of technical skills.

  4. Like Florian, I agree that maths aren’t just another tool in the box (could one argue the same for writing?), but are an increasingly important part of ecologists’ daily lives. A former supervisor had to send off punch cards by bus and then wait 2-3 days if he wanted to do anything more complex than a two-way ANOVA. Today, we can run any of a myriad of statistical processes in minutes from the comfort of our office or even our home! As a consequence, if I was getting into something as simple as a generalized linear model, he was little help and I was on my own.
    Having to teach myself was very valuable for me, but drove home two points: quantitative skills are often taught poorly, and are increasingly essential to make sense of an increasingly quantitative ecological literature. Even the nested hierarchical relationships between a t-test, ANOVA, general linear model, and generalized linear model (all of which aren’t really examples of statistical machismo, but I would consider routine) are lots on many of my cohort.
    If new ecologists don’t have a handle on how the data are analysed, how can they read the literature critically?

  5. From the WSJ article: “I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail.”

    Apparently, these bright young undergraduates thought that gaining strong math skills was impossible for them. While still undergraduates! Unfortunately, Wilson’s article is a disservice to the bright young undergraduates that are willing to improve their quantitative skills and would benefit from doing so. In other words, the majority of bright young undergraduates.

    • Agree 100% Amy. Wilson’s notion that *Harvard* students of all people can’t be taught some quantitative skills or to love mathematics would come as news to some of Wilson’s Harvard colleagues:


      And remember, this is coming from a guy who once co-authored a population biology textbook that has the usual amount of math in it! For the life of me, I can’t understand how Wilson of all people could possibly say much of what he says in this piece.

  6. Jeremy, I think you’re over the top on this, especially with some of the language (accusing Wilson of “pandering” and so forth).

    Wilson is simply saying that there’s more to understanding a phenomenon than having a mathematical description thereof, and I absolutely agree with him on that. Darwin/Wallace are the obvious classic case on that front, but they’re not alone. Mathematics/statistics are just languages in the end–the language of quantification. They may or may not help one to conceptualize any given phenomenon under discussion, depending on several particulars, which include, at least, how one’s own mind conceptualizes things, the exact expression of the mathematical notation in question, and the context of the discussion.

    Mathematics is just an abstract depiction of some aspect of reality. Of course, that’s true for all language, but math is a very highly refined art, and not the basal way the human mind conceives of patterns and processes. Children don’t naturally do calculus or algebra, but they can tell you that ten balloons are more than one balloon, and that a rabbit is not a cat without knowing which is called which. Math/stats are refinement tools, nothing more. They’re powerful tools when used correctly, and when applied to murky/noisy problems one can make some probabilistic statements about cause and effect that one otherwise couldn’t, but that doesn’t mean they’re necessary for understanding the gist of everything, or possibly of *anything*. I think Falco summarized the issues quite well above.

    • And my original post on the zombie IDH (now a paper in TREE) illustrates the sort of trouble that *really famous ecologists, *entire subfields*, and *textbook authors* can get into if they don’t know the sort of basic math I teach to my undergraduate population ecology students. Most people’s untrained intuitions about how ecology and evolution work, or how to design an experiment or infer a conclusion from it, are rubbish. I know you’re joking, and I don’t mind that–but there really are serious issues here.

      Look, there’s no one level of mathematical expertise that everyone needs to have to succeed in ecology. And yes, different ecologists absolutely have different strengths, and it’s fine for different ecologists to take different approaches, well-fitted to their own skills and interests. But the notion that if you’re not good at math or don’t like it, you’ll be fine and don’t need to progress beyond what you learned in high school, because you can just seek out subfields or topics where your lack of math won’t be exposed, just isn’t true, at least not very often.

      Indeed, it’s not even how *Wilson himself* made his way. He likes to emphasize his own weakness in math and dislike of the subject. But *as a Harvard prof* he went and took undergraduate calculus classes *on his own initiative* because he felt like that was a gap in his background that needed filling. That is not the action of a man who sincerely believes that you can do great things in biology no matter how much math you know. Wilson became comfortable enough with math to co-author a population ecology textbook. He became comfortable enough with math to appreciate and understand the models that his many collaborators developed. And so on.

      p.s. Wilson’s Harvard colleague Steven J. Gould provides a nice illustration of how you can go off the rails if you don’t know enough math to make a major contribution, but mistakenly think you do:


      Part of the problem with not knowing math is that you’re often not well-placed to identify questions on which someone lacking mathematical training can make a substantial contribution.

  7. I think this is one of the worst essays I’ve read in a while. Riddled with logical fallacies. The basic argument seems to be: I don’t have property A, and am successful, so not having property A isn’t a bad thing. Or take this: “Pioneers in science only rarely make discoveries by extracting ideas from pure mathematics.” and then this: “Real progress comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone. Eureka moments require hard work. And focus.” How on Earth does Wilson think theory is produced? Does he surmise that mathematical theory just floats down with the sun rays when you are sipping you cocktail by the beach? It’s annoying that he seemingly pitches age-old platitudes about creativity and hard work as an alternative of learning to do math.

    Not surprisingly, I agree that this is very bad advice. It is true that you don’t necessarily need to become a mathematician to do good biology. Everyone out there has to judge for themselves which skills are important to their career and intellectual development. So, I don’t have any problem with encouraging people to pursue science even if their math skills aren’t what they could be. What I do have a problem is the assertion that not knowing math is actually not a loss based on a deeply flawed description of the role of mathematical theory. Make no mistake: you can be a good scientists without good math skills, but you’ll be a better scientists with good math skills. This is why this article is so pernicious: it seems to say to prospective scientists that it’s ok to let your math deficiency stand. And it does so by denigrating the role mathematical theory plays in science. It’s not a recipe for success as a scientist, especially as biology has now reached a level where mathematical theory can actually be brought to bear on complex empirical phenomena.

  8. I thought Wilson’s piece was mighty good, though susceptible to the overgeneralization that happens when he stretches beyond his realm. For the record, even though I’m an ant guy, I’m not his biggest fan by any means. (Perhaps because I’m an ant guy, if you Pheidole my meaning.) That said, anybody who works on ants is aware of how much of our progress has been to him alone.

    This was his main point in his op-ed: you can be an awesome scientist even if you’re not a math guy. And he’s right. Exhibit A is himself.

    When he brought up the fact a modeler needs to know the possible permutations that might actually exist, I didn’t read this as a knock on experimentation, but instead, an emphasis that the models actually have to have something to model. George Oster could never have cooked up the Caste and Ecology in Social Insects ideas without Wilson working with Oster to explains what happens on the ground inside ant colonies. The models which he would have made wouldn’t have been relevant to the questions at hand. He’d cook up all kinds of permutations that wouldn’t include what really exists, and would do little to inform what really exists. What makes Oster&Wilson so bloody damn useful so many years later is because it is a unique merge of theory and natural history that is lacking in so many models. Models are theoretical, but they are created about things that actually exist. The more you know about those things that actually exist, the more you can get out of your model and the more the model will make sense.

    Let’s face it, Wilson is more famous than all of the other ecologists mentioned here (MacArthur, Hamilton, Haldane, May, Chesson, Tilman). The others are favorites of ecologists (and behaviorists maybe) but whose ideas stretched beyond their field to have a broad mark? Wilson. That’s the point behind Wilson’s piece, but he doesn’t want to be a person to brag about it. The math people can come up with all of the fancy models, and all of the experiments to test the ideas. But where do the ideas come from, who develops them in the first place? That really doesn’t require a ton of math. Wilson had gotten generations of math people to do his work and put flesh on his theories, and worked with the math folks (Oster, MacArthur) to get ’em started. The same goes for the taxon cycle, too.

    Erol is partially right – he’s spouting platitudes about creativity and hard work being important. He’s not saying that they’re more important than the math. Wilson is just saying that you can still be a scientist without it, and that creativity is an essential element that gets overlooked.

    His piece is autobiographical – you can’t argue with the fact of what he’s done and where he is. Is that the model for future scientists? It shouldn’t be. But, if all kinds of high school students and college students see this and think that not being a math person should entirely rule out science, then it’s a good lesson to learn. Some of my best students weren’t, at least at first, mathematically inclined. But they had an incredible set of intuitive skills, and – yes – a hard work ethic, and they were very able to develop and criticize ideas. They then struggled with the math behind it, but that indeed isn’t preventing them from becoming good scientists.

    Of course, this piece also shoots himself in the foot when it comes to Nowak et al., which is entirely built on a complicated model – if Wilson didn’t have big hand in it, then we shouldn’t be too sure about whether it makes much biological sense. But in this case, the purpose of this paper was not the model itself, but to shake people out of the kin-selection-must-be-right-and-nothing-else-can-be mindset. That mindset is flawed, because a lot of the predictions.

    While empiricists might be attacked for sticking to their guns in the face of math, Wilson has been dealing with the polar opposite: the modelers and the math people keep sticking by kin selection as the only evolutionary force behind eusociality, even though the empirical evidence is kind of equivocal on the matter and doesn’t support it as much as it should given the predictions of the theory. The theoreticians don’t want to go back to the drawing board and model group selection as a genuine possibility, and to figure out how this might actually work in reality. The modelers doth protest too much.

    The world is even more mysterious than it was in the time of Darwin. There are still many things that are fundamental that we don’t know. It’s been only in relatively recent years that we figured out how eukaryotic cells emerged, for example, and only more recently that we’ve sorted out the function of the appendix. There is a ton of room for people who have ideas, and do science to market those ideas and get others to test them rigorously. Are modeling, math, and rigorous tests of complex theories necessary in science? Of course they are. But does everyone have to be like this to be a great science? Hell no. That’s Wilson’s point. And until you wish Wilson off the face of history, he’ll still be right.

    • As an explanation or caveat, keep in mind that I’m reading this editorial the way that I read much of which comes from Wilson: he has a point he wishes to make, which is typically a good and important one, and then he overstates it to a certain extent. This has the effect of invoking skepticism and criticism and starting a conversation, and when the conversation is over, Wilson’s argument is then scaled back to where it should have started. If he merely started, at that point, though, the conversation would never have emerged at all.

      So, of course he underemphasizes the importance of math more than he should in the training of a contemporary scientist. Once you peel away the obviously stupid things, though, his point is mostly right about not needing to be a math genius to be an effective scientist that makes a difference.

      After all, if he didn’t start with the bombastic statements, we wouldn’t be arguing about it now. It’s a great lesson in careerism. (It worked with r* too.)

      (By the way, if you’re reading this Ed: Hi!)

      • Re: Wilson’s rhetoric, sorry, gonna disagree with you on that too. It’s not that he couched a fundamentally-sound argument in deliberately-provocative rhetoric. He made an unsound argument. I’m all for rhetoric in scientific writing–so long as it’s at the service of good arguments, rather than a substitute for good arguments or a disguise for bad arguments. And I don’t think you can defend a provocative bad argument by saying “hey, at least it started a conversation”, for two reasons. First, provocative *good* arguments are equally good at starting conversations. Second, if the ultimate goal of the conversation is to give good arguments an airing, it’s needlessly roundabout to start with bad ones.


      • I agree with you entirely. It’s not a good way to argue or to do science. It is, though, Wilson’s way. So I read it with that lens. I’m no Wilson apologist. Info find it funny that we’ve all put 2000% more time and thought into his piece than he did. I hope he reads it again next week and is a little embarrassed.

        “Don’t sweat the math” is a horrible message. I’m admittedly inclined to appreciate his implicit message, that an overemphasis on using theory as a tool for discovery has its limitations. Hamilton was an excellent natural historian, by the way, and his ideas emerged from observation as much as anything else.

      • Yes, Hamilton was an excellent natural historian. Although just to make sure nobody gets the idea that you have to be in order to do theory relevant to empiricists, I’ll point out that George Price wasn’t a good natural historian. Indeed, he wasn’t even a biologist.

      • And yes, I’m sure we are reading Wilson through different lenses. That’s a good point. I’ve never met him, or read a great deal of his stuff (read his autobiography back when it came out, but don’t remember it much). When I read him, in the back of my mind are other senior, empirically-oriented ecologists who’ve said ridiculous things about the role of math in ecology:


    • Thanks for your comments Terry–Wilson couldn’t ask for a more generous reading or a more articulate defender of his piece.

      Yes, the intended point of his op-ed is surely that you can be a great scientist without being a math guy–it’s still a live possibility. But as evidenced by many of the comments here and on Twitter, his op-ed does a very poor job of making that point. For instance, if that’s your point, why would you take time to argue at length that most theoretical work is useless, and to claim (falsely) that the only models that are useful to empiricists are those that describe the world as it actually is? Why would you clutter up your editorial by talking at length about daydreaming, about how good ideas “follow from thorough, well-organized knowledge” as opposed to from math, and about how “real progress” comes from field notes, hard work, and focus (the perhaps-unintended-but-nonetheless-obvious implication being that mathematicians lack those things). Why would you claim that it’s a “general principle” (not “something I personally have found to be true in my own undoubtedly-unique life” but a general principle) that it’s easy for a mathematically-ignorant empiricist to find collaborators, but hard for a theoretician to do worthwhile work on his own? Why, when listing fields in which mathematical skill is needed to make significant progress, would you specifically exclude all of biology save for a few specialized molecular fields? I’m sorry, but if Wilson’s intent was simply to throw his own example out there as one under-recognized possibility among many–which I emphasize I would’ve had no problem with–he did a lousy job of it. So sorry, I don’t think it’s a great piece. It’s a bad piece. I think someone else–like you!–should write the piece that this piece should have been. Seriously–you should do it! You may not have Wilson’s fame. But I bet you could do a much better job than he did of making the case for the sort of science he was trying to make the case for, without denigrating other sorts of science, and without overgeneralizing from unique or questionably-relevant examples like Darwin or Wilson himself.

      Re: the purpose of models, there are lots of different sorts of models, constructed for lots of different sorts of purposes. Here’s a partial list. And here’s a great paper on all the ways in which false models are useful to empiricists, and how they’re useful precisely because they’re false. And here’s Hal Caswell’s classic 1988 paper on the various roles of modeling. No, I wouldn’t expect Wilson to get into any of this in his piece. But nor would I expect him to perpetuate howlers like the idea that models are only useful if they describe the observed world as it is, in all its glorious detail. Nor would I have expected him to implicitly (and presumably unintentionally) denigrate the creative and original contributions made to his work by his own collaborators. In his autobiography, he’s far more articulate and generous about how his many collaborations worked and what his collaborators brought to the table, and I don’t think he ever says or implies that collaborators are easy to come by, as he does in this piece.

      Another problem with Wilson’s piece is that it doesn’t even acknowledge in passing that all branches of science, including biology, are more quantitative than they were back in his day (not to mention Darwin’s day!), and that they’re becoming more quantitative all the time. Do we want to scare off students who don’t go into biology with a pre-existing love of math? Of course not! We’d be scaring off most of our students–students who are really into math mostly go into mathematics, or physics, or engineering. But it does those students a tremendous disservice to tell them that, if they don’t like math or if they struggle with it, that’s ok, they can just seek out one of those corners of science where one can make a really big fundamental contribution without knowing any math. That just gives them an inaccurate impression of what science is like these days. Far better to tell students that we’re increasingly less data-limited, and so we’re increasingly more ideas-limited. It’s more important than ever to ask good questions, to think of good ideas. Good questions and ideas come from being broadly-curious, broadly-knowledgeable, and broadly-trained–including in subjects which you might not have a pre-existing inclination to pursue. Because after all, what are the odds that it just so happens that the stuff you most like studying is the stuff that’s going to prepare you to come up with a really good idea?

      And if you want to make doubly-sure that you don’t unintentionally scare off students who don’t like math? Tell them what I tell my undergraduate population ecology students: “Look, I know you probably aren’t big on math, and that you probably find it hard. But you know what? Mathematics is a tremendously powerful tool for thinking about the complicated world we live in. Getting to grips with math will make you waaaaay smarter. You’ll not only be better able to evaluate your ideas and avoid mistakes, you’ll actually think of more, different, and better ideas than you would have otherwise. Even if you never get nearly good enough at math to be a modeler, you’ll be better off than you were before–you’ll see the world through new eyes. Every single person in this room can get to grips with this material. And you’ll probably even enjoy it, or at least enjoy it more than you thought you would. Will it be challenging? Sure. But if it weren’t challenging, it’d be boring. And I’m sure you don’t want to be bored.” And then back up that beginning-of-term statement by interweaving math and biology throughout the course so that the students learn how helpful and how cool math is at ever stage of the scientific process. Taking his op-ed at face value, that is not what E. O. Wilson thinks we should tell our students, and it’s not how he thinks we should teach them. So who’s right? Me or him? This isn’t a rhetorical question, I really want to know what you think. Because this issue–how we teach our students–is really the big substantive issue here.

      Couple of minor comments:

      Re: the reception Nowak et all. received, I more or less agree with this. This old post has some links to relevant, and less snarky, commentary.

      Re: Wilson being more famous than everyone I named, maybe with the general public. But it’s Hamilton who’s most often named as the greatest evolutionary biologist since Darwin.

      • Upon a reread of the Wilson piece, I’m finding that I like the thesis plenty but find the arguments are lacking.

        Real progress does come from field notes. But math is the language of science, and you’ve got to speak the language.

        There is a whole genre of natural-history-is-dying editorials that come out at a steady rate. They are mostly half complete in their vision of the consequences of this phenomenon. This is partly related to Wilson’s point, and he’s not connecting the dots as he could have, and using just himself is poor argumentation.

        I indeed have had plans for writing about it, but I’ve been reluctant to tackle it soon for the time it’d take. In the meantime, I’d encourage all students to devour models and math, but for the sake of us all, do it outdoors.

    • “Whose ideas stretched beyond their field to have a broad mark?”
      Haldane’s. (And he was just as adept a populariser of science.)

  9. I think an editorial like this does more harm than good. In my experience it is more common for undergraduates to have the perception that strong mathematical abilities are not critical for a career in biology. This belief is reaffirmed via the limited use of math in many undergraduate biology programs.

    While people differ in their inate abilit to grasp and use mathematical concepts, as with most most things, a lack of talent can be compensated for by practice. This surprising editorial just gives an additional excuse to avoid math: “Hey, Wilson and Darwin didn’t need math, neither do I.” I think the more important message is, the more time you spend improving your math skills now, the less you have to play catch-up later.

  10. Have not read all comments so perhaps someone has said this but there is a HUGE difference between being able to do pure math in your head & the ability to render physical pictures of models in your head. It takes years of problems sets to make a theoretical physicist, and they are slightly different than pure math folks. (I know this because I tend to only date dudes who know more quantum mechanics than I do, my BF is a hard core molecular orbitals guy.)

    A lot of bio folks are more verbally orientated (as am I). We do not need to know string theory, but some math ought to be required. Esp. stats. (I have personally found knowing linear algebra and quantum mechanics quite helpful for understanding my Raman and infrared studies toward tumor diagnostics). OK must dash and talk to the MDs now.

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  12. Excellent piece. Math is critical, it’s essential, it’s a must, it’s a can’t-do-without.

    Just the same, the math doesn’t give the answers. We think, we observe, we do math, then think again, observe again and do more math. All scientists need to constantly reassess their thinking on the basis of both math and general principles.

    And I so, so, so agree with your point about science in the 21st century.


  13. Wilson’s thesis is: don’t leave science if you’re not good at math. Fine, but why isn’t the answer “become reasonably good at math”? It is a skill, not a talent.

    Wilson makes the analogy to fluency in a foreign language, and it’s appropriate to take that analogy farther. Math is the language of the universe. Why excuse ignorance in that language? A fun trick is to take all the instances of “math” and replace them with “language”. What if Wilson had said “I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong [language] skills, they would fail”? Is that acceptable?

    If you are a scientist who struggles to read and write in your language (or nowadays, English), can you still do science? Of course. But if you never learn to do so well, you will struggle mightily to understand the ideas of others and make your ideas known to the broader community. No professor should accommodate a recommendation that his students simply accept substandard communication skills, and instead seek collaborators who know the language. No: if they want to be better scientists, they should strive to be better writers, better speakers, better communicators. In language, and in math.

    Wilson also does not address all the basic scientific mistakes made as a result of mathematical ignorance, over and over again. Easy enough to say “find a collaborator”, but the hazard arises when you think you know enough and misinterpret your data as a result.

  14. Hi Jeremy. In essence I wonder whether it’s true that in general, ‘quantitative types’ tend to over estimate the importance of maths and downplay the data collection and observation side of things, and those who are less quantitative and more focussed on the natural observation of ecological systems and data collection ‘field types’ are guilty of underestimating the importance of maths?

    In the end, clearly polarisation and categorising people into boxes doesn’t help anyone. Not knowing E.O. personally, I can’t be 100% sure of his motives for such a piece, but he clearly cares a lot to stick his neck out like this. Lindenmayer and Likens have made similar points elsewhere http://www.esajournals.org/doi/full/10.1890/0012-9623-92.3.245 , which from my reading of it appears to be a push back against a real or perceived concern for increased emphasis on numbers and the latest modelling techniques in ecology and a view that ‘traditional’ ecology is now old fashioned and not of the same value. I have heard some very prominent ecologists say ‘If you don’t understand formula X then you are not a real ecologist’. Clearly this attitude is just as damaging as some of what E.O. has said.

    Either way, can I also say that I found your post (reply) greatly disappointing, not because of your different viewpoint, but because of your approach. I was an avid reader of Dynamic Ecology when it first started, but am becoming increasingly turned off by the tone and cheap point scoring that is becoming a feature of many of the posts here. I hope we can move towards robust but more respectful debates.

    Euan Ritchie

    • Thank you for your comments Euan.

      I’m of course disappointed that you don’t like the tone of this post or others, though in light of that I’m surprised that you used to be an avid fan. Many of my earliest posts, back when I was still with the Oikos blog, take much the same tone (e.g., my “zombie ideas” posts, or my post on the Spandrels of San Marco). As for whether the critical posts here make substantive points, or just aim to score cheap rhetorical points that don’t stand up to scrutiny, all I can say is that I’m aiming to make substantive points, with the rhetoric being in support of substance rather than a substitute for it. But again, I certainly recognize that my tone and rhetoric in this sort of post won’t be everyone’s cup of tea. I write the way I do for several reasons. It’s my natural voice–I like a good argument, and I have a snarky sense of humor. Lots of people seem to like it, or at least not mind it. Early on, when I first started blogging, I did several posts where I worried about the tone, and got very positive feedback, including in one case from the ecologist criticized in the post. It’s a voice that’s well suited to blogging as a form, I think, though of course it’s far from the only voice that is. And there’s no one voice that would please everyone–some readers find a measured, snark-free voice boring, and some readers think that any criticism of a fellow scientist’s work is inherently rude. So I just write in my natural voice, and reluctantly live with the fact that some potential readers will be turned off.

      None of which isn’t to say I haven’t ever crossed any lines that shouldn’t be crossed, or that I don’t ever worry about my tone. You’re not the only reader who’s told me publicly or privately that they find my tone a big turn-off. And I’m very aware that anything I write online will shape how people see me offline. I don’t want anyone to see me as a jerk, and it does bother me that there are now at least a few people (only a few, I think) who do see me as a jerk because of my blogging. And I did worry a little about this post specifically, in part because Wilson’s tone was very polite. In the end, I decided it was ok, because while Wilson’s tone was polite, his substance really bothered me. He went out of his way in the Wall Street Journal to say that more than 90% of the work of his theoretical colleagues is useless. Not just not useful to him personally-useless, period. And as you can see from the comments on this post and on Twitter (search on “dynamic ecology”), lots of people (by no means all, but lots) were similarly bothered. So in this particular case, I think the tone of this post merely gives voice to what many ecologists felt. Now, one could of course argue that even if I and many others feel that way, we ought to suppress our feelings and bend over backwards to keep the tone civil. But part of the attraction of a blog for me, and for many readers, is the opportunity it provides to be honest and open, and say what you really think or feel. That’s an opportunity the scientific literature doesn’t provide. I recognize that you may not see it this way, but for me posts like this one are very much of a piece with posts like the one where I talked about how I almost quit science, or the one where I showed my “shadow CV” (listing all the papers I’d had rejected, all my grants that didn’t get funded, all the jobs I didn’t get, etc.) Of course, readers might reasonably disagree about how much honesty and openness is too much.

      It’s possible I’ll decide to stop writing this way in future. I’ve actually been consciously avoiding writing this sort of very forceful post for a little while. I worry that if I wrote this sort of post all the time, more readers would be turned off. Andrew Gelman recently decided to stop using snarky humor in his posts because he felt it was getting in the way and too many readers were misunderstanding his posts.

      Given your views on the tone of this piece, I don’t imagine that you’ll like what I had to say about Lindenmayer and Likens back when that piece was published…


      • I’m hearing a lot about “tone” from the biologists. Noticed bio folks tend to be highly extroverted people who really like being nice to everyone around them. They like being popular and well-loved. They don’t like to see people fighting and love team sports.

        I took a lot of classes in college with the biologists, but I went to parties with the physicists and mathematicians. They tend to be introverted folks capable of quietly sitting for hours and hours entirely focused on a problem set. They tend to dislike large crowds & prefer books over people. They are also the funniest people I have ever met. They love a good debate, and tend to use amusingly abrasive “jokes” to “win” conversations. I frequently use this as a teaching method when talking to the math guys I know. They tend to think very, very quickly; and if they are thinking in the wrong direction I stop them via insulting them and showing them the correct direction. They actually appreciate it; they don’t like to waste time thinking incorrect things and are usually convinced that they are always right all the time!

        Meanwhile, when I teach biologists, I usually gently show them what the correct answer is, and then have them repeat it until they have understood it. If they are wrong about something, I usually communicate non-verbally that they are incorrect.

        Biology is at a point as a field where it NEEDS math and physics. The optics are just at the point where we can start to get quantitative imaging information from single cells. We need to start to understand the physical model for how life works on an atomic level if we are going to truly provide things like effective therapies for cancer. This requires math, chemistry, and physics.

        Biologists of a certain age still recall the good old days when one could stroll into the lab and discover, say, a new protein, gene, or some novel animal behavior. Only one scientist was needed. This has changed. The biologists need to let the math folks have …. fun amongst themselves, and not accuse them of being “mean” when they are addressing their own audience. The math and physics folks need to be a bit less abrasive when interacting with biologists.

        Universities are starting to encourage inter-departmental collaboration (SBU did this a lot). But the bio & medical departments need to realize that they will have to hire stats profs; handling the amount of data generated by the Big Bio experiments is a full time job. They’ll have to hire us analytical chemists as well, to ensure proper trial design & reproducibility of results.

      • Wow Allison, that’s an amazing comment–lots to digest! Don’t know if I can really do it justice.

        Very interesting remarks about the sort of people you’ve found to be attracted to biology vs. physics or math. My own experience socializing with mathematicians and physicists (as opposed to ex-physicists who turned to biology…) is far too limited for me to compare notes with you, unfortunately. I guess I’ll I’d say is that there’s obviously a lot of variation within each field too. Within ecology, I’m certainly an outlier in being as intellectually combative as I am. I think fast, too. And while I don’t intend the jokes I make to “win” conversations (I intend my evidence and arguments to win), I can see how they’d come off that way.

        It’s perhaps an illustration of your “cultural” remarks that biologists sometimes complain that their own field is *too* combative:


        The other thing to note is that mathematics and physics types were early adopters of the internet as a means of communication and discussion, and to an extent that’s shaped the behavior of everyone who reads and writes things online. Those fields also tend to skew more heavily male than biology (as the readership of this blog does, to an extent that shocked me when I discovered it via a reader survey), and of course certain ways of behaving tend to be correlated with gender. And readership of blogs tends to skew young (our readership is about 40% grad students, 30% postdocs, 20% faculty, 10% “other”, for instance), as of course do certain ways of behaving. All of which probably helps explain why most of our readers find the tone of a post like this one to be fine, while a minority find it really off-putting.

        It’s interesting to think about whether these sorts of cultural differences actually have substantive effects on the progress or direction of science. Do you think they do? Is there some “optimum” level of, say, “combativeness” or “enjoyment of a good argument” that a field as a whole (or even individual scientists?) ought to have? Or is it totally a matter of different strokes for different folks–there’s tremendously wide scope for individuals with any given personality to succeed in any field, and tremendously wide scope for a successful field of science to have anything from a “math-like” culture to a “biology-like” culture? I have an old post that’s sort of about this:


        Re: biology needing math and physics, I broadly agree. And I think that’s increasingly widely recognized. Certainly in ecology, “Big Data” and the sophisticated quantitative tools needed to analyze it are becoming increasingly prominent. Ecology is also becoming more collaborative. There are more and more big collaborative groups working on compiling and analyzing existing data (an approach pioneered in ecology by NCEAS). And there are more and more big collaborative groups pursuing “complex” and “interdisciplinary” (and “expensive”!) research projects. I’ve mused in the past about whether these trends select for certain personality types:



      • @Jeremey

        Yeah, I started in a fly lab at the Hutch in Seattle when I was 15 and sort of strayed into laser spectroscopy for protein analysis and tumor diagnostics. I’ve met a looooot of different kinds of scientists along the way.

        There are some gender differences. Have noticed that groups of men tend to act like a pack of wolves- there’s a strict hierarchy & lots of fighting, but the fight has rules. No one actually gets hurt (usually). Groups of women tend to behave more like a pack of deer, there’s a shared watchfulness for predators. There’s an acute awareness of the external environment. There’s no fighting, there’s sharing. Exclusion from the group can mean death; whereas while lone wolves might be lonely, they still have a decent chance of survival. (Watched too much Attenborough as a girl, heh.)

        One of the students I had in Germany a couple years back was a guy about my age (I was 28) who was doing his Master’s thesis project with me. He’s a chemist. I sent him upstairs to the tissue culture lab to meet fellow students for a lunch. These labs are populated almost entirely by women. He came back down about an hour later. His hair looked a bit frazzled, and he had a certain, desperate look in his eyes. He looked me straight in the eyes and just said, “Those girls….talk….a *lot*.” I nodded and said, “Yes. They are cell biologists. Now get to work.” And he spent the rest of the afternoon in cheerful silence taking spectra from a range of plastics while I worked up a powerpoint for a departmental seminar.

        I’m a girl, so I don’t mind the talking as much and love having long chats with my girl friends. But I am also an introvert, so I can appreciate that constant chatter is not everyone’s cup of tea.

        Winning a conversation is more prevalent in my generation, I suspect. We grew up with the internet and it’s more natural for us to have 5 IM conversations with our friends all at once rather than to pick up a phone and call them in serial. Since the internet removes the “body language” component of the conversation, it can get quite…rough. (Ref.: 4chan.)

        I very much think you’re on to something with math-like vs bio-like cultures. Math is …… not a team sport. You can either do the math in your head, or you can’t. Everyone should be able to do a certain amount of math, but it should not be shameful to not be able to do algebraic topology!

        Meanwhile, biology IS a team sport; and it’s important that everyone on the team gets along. Tone can be important. Think certain folks in biology are more used to wolf-like behavior, whereas others want deer-like behavior. If done correctly, both behaviors can bring the field benefits. Diversity is needed in the science ecosystem! Clones tend to get wiped out by the first pathogen that they encounter!

      • Thanks for such an honest and candid response Jeremy. I appreciate we all have our own individual styles, that is fair enough. I also enjoy a good argument, but I don’t think this need necessarily involve language that could be categorised as overly harsh or inflammatory. In fact, often when I see this it’s a sign to me that those making the arguments are lacking substance and support for their statements and compensating in other ways. Why should I care about all of this? I care because what example does it set for our students and the future leaders in the field? Does the world not have enough debates full of harsh language, personal attacks etc (see current Australian politics for a good example)? I think this blog post http://thesiswhisperer.com/2013/02/13/academic-assholes/ is very relevant here. Like I said at the start, there’s some terrific stuff on DE which I really enjoy reading, great job and keep it up, so why compromise that with an overly abrasive tone?

    • Euan,

      The only critical or negative things I’ve read in Dynamic Ecology are directed at ideas, and not people. We all think the way we do things is the best way. If we didn’t think what we were doing was best, then we’d change over to whatever we think is best. There’s clearly a copious amount of confidence, but I think it’s done in a tone of respect. I think a focus on civility is always good, but I don’t see a shortage of it here. Actually, I think if other ecologists heavily biased against empirical work were to follow the model here, our community as a whole would be better off.

  15. I’m reacting to your update note. I thought your original post was fair and on target and didn’t have anything to add because you said it well.

    I think a real road block in the sciences (and biology especially) is that it is seen as uncool=nerdy to be good at math. Therefore even people who are pretty decent at math (like your top undegrad or EO Wilson himself) profess to be bad at it. This goes on everywhere from high school hallways to national politics. And it leads to people say things about math that they would never say about English or writing. (“I just don’t get that writing stuff – it’s too hard” – people would get put in their place if they said that, but it is fine to say about math). When was the last time you heard a national politician say “I’m a terrible writer”? You don’t hear it – it equates to saying I can’t think. But politicans (and again EO Wilson) stumble over themselves to say they’re bad at math. Who would vote for a math nerd? For those of us who are older remember how Ross Perot got painted as a crackpot because he kept pulling out graphs during presidential debates? But this is ultimately just a facade based on social norms, not reality.

    And re the whole Wilson claim. Ask ecology or evolution graduate students if they wish they had more quantitative skills and 90% of them will say yes. Unlike the socially driven public professions I mentioned, this is an honest window into reality. And it is pretty decisive.

    So come on people, get over your social hang ups! Be out and proud! Math is cool and not incidentally critical in biology.

    • This is why I invited you to join Dynamic Ecology Brian–rather than reigning in my own combative impulses, bring on board someone even more combative than me, so that I’ll look wishy-washy and agreeable by comparison! 😉

      I don’t actually agree 100% with you here. I do think you’ll hear people, both within and outside science, be self-effacing about their writing skills, and indeed about all sorts of things. More broadly, I don’t know that I’d connect Wilson’s piece to the anti-intellectual streak in broader American public life. Not that there’s no connection. But I think the broader anti-intellectual streak that you rightly recognize has other, more important roots besides the sort of math phobia that afflicts some empirically-oriented biologists and biology students.

      • Happy to make you look “wishy-washy and agreeable”.

        While, I agree there is an anti-intellectual streak in America, I was referring rather specifically to an anti-math streak which I think is even stronger. I’m pretty sure math is cool in Russia or Hungary or China so it is a cultural norm. It’s going to cost us as a nation ultimately. And it is costing us (internationally) in biology.

      • It’s definitely true that weakness in mathematical biology is causing other nations to do things better than we do in the US. The amount of mathematical literacy required of a person with a Bachelor’s degree in the sciences is rather sad. The same is true of high school graduates, actually.

  16. I think you’re overly and unnecessarily chaffed over this issue Jeremy. Definitely. The problem’s not just your tone, which is a problem, but the several mis-characterizations of Wilson’s position, beginning with the title of the piece, which is clearly wrong.

    • Hi Jim,

      As to whether I’m overly and unnecessarily chaffed, all I can say is that if I am, clearly many others are as well, judging by the bulk of the comments here and on Twitter. Of course, we could all be overly and unnecessarily chaffed. But when lots of smart, informed, well-meaning people are all chaffed about the same thing, that at least suggests that they have good reason to be chaffed.

      As for my tone, I agree that it skirts close to the line. Brian and many others think it’s 100% fine, and even find it entertainingly forthright. But a larger minority than usual seem to find it over the top. Having re-read the post more than once, I’ve decided to leave it as is rather than edit and apologize (as I have done in the past when I’ve posted something and then subsequently decided it crossed a line). But I will probably do a follow-up post soon, talking more generally about why I sometimes write in this style and asking for feedback on the general tone of the blog. Not really because I’m worried about the tone, either of this post or more generally–as I said to Euan, you can’t please everyone–but because I believe in being open about what I’m doing and why I’m doing it, and because I’m far from infallible and I do care how people react to what I write.

      As I’ve indicated in the updates and in response to other comments, I agree that Wilson surely intended his piece as autobiographical, and for his autobiography to be an inspiring example to math-phobic science students. But I stand by my claim that his piece functions poorly as inspirational autobiography. If you’re writing inspirational autobiography, there is no need to go out of your way to talk about how you think over 90% of theoretical work is useless because it doesn’t describe the actual world, and about how you think “real” insight hardly ever emerges from mathematics. None of that stuff has squat to do with Wilson’s own autobiography, or with inspiring math phobic students (unless he’s trying to encourage those students to continue on in science because they’ll be the ones doing *real* science, not like the useless hypothetical crap that comprises >90% of the work of their mathematically-inclined fellows). It’s just Wilson denigrating colleagues who work in a different way than him.

      I also stand by my claim that Wilson is overgeneralizing from his own autobiography. What worked for him is, I think, very unlikely to work for most others, especially these days when every field of biology is becoming more mathematical (an important trend Wilson fails to note). Even if you’re just throwing yourself out there as an inspirational example of what’s possible, I think it is incumbent upon you to be more aware than Wilson is in this piece of whether others are likely to be able to follow your example. Since encouraging others to *follow* your example is the whole point of presenting your own example in the first place.

      I also stand by my claim that Wilson is misdescribing his own example. No, he’s not a theoretician. But he knows as much math and stats as a typical empirically-oriented ecologist or evolutionary biologist–i.e. far more math and stats than the average undergraduate biology student knows. It is simply not true that math-phobic biology undergrads can go on to do important science in any field of biology

      Finally, as I decided not to note in the post, but as other commenters have noted, Wilson himself arguably is a bad example of finding a niche where one can do fundamentally important work without needing to know math. He added his name, with all the weight of authority that implies, to a *very* polemical, and heavily mathematical, Nature article (not a letter to the editor, a peer-reviewed full-on article) on the evolution of eusociality. Wilson’s name is on there even though by his own admission he almost surely doesn’t understand the math in the paper. I do think this is a telling illustration of just how difficult it is in practice to follow Wilson’s advice to find some unexplored niche where one can make important contributions without knowing math.

      Re: the post title, as a long-time reader, you know that I aim for punchy titles that will attract readers. I think this title is fine; it summarizes the content of the post as well as any short title would. I trust readers to read my posts and judge them accordingly, not judge them by their titles.

      • Jeremy, no.

        First, I have < zero sympathy for the "everyone else is doing it too" argument. That's an illogical line of defense. And I'm sure not going to spend time chasing down what people are saying on Facebook or Twitter or those other links you gave. I don't really *care* how many people are supposedly agreeing with you, especially since I don't think you're particularly objective in your judgement on this issue in the first place.

        I wasn't talking about the title of *your* piece, but the title of *Wilson's WSJ piece*. Your claimed title distorts his meaning, which is: being a great scientist != to being good at math. He is NOT SAYING that great scientists don't need math. You have replaced his intended meaning, with a straw man characterization of it. It's not accurate, pure and simple.

        Wilson has an entirely valid point that conceptualization of issues can be largely free from mathematics, a point which I heartily agree with, but which has otherwise been trampled under foot in the rush to crucify the guy. As Manuelinor correctly notes below, Wilson is referring to *exceptional* mathematical abilities as what are not necessarily needed to succeed in science, not saying no math ability is needed at all.

        Maybe Wilson was flippant or cavalier with what he said, or provocative. Fine, maybe so. But don't make a federal case out of it.

  17. I find Wilson’s piece encouraging. Nowhere in the piece does he explicitly say that you don’t need math to do ecology – he makes repeated references to increasing knowledge, learning maths later in life, and (in particular, para. 8) that maths and statistics are required to advance any theories/concepts you may have come up with from intuition/ideas.

    When he refers to ‘below-par’ maths skills being enough to make it, he is talking about “exceptional” maths (his word) – not ordinary, basic-level math skills. There is a huge difference.

    Many of you are talented quantitative ecologists who can get your head around complicated formulae, equations and symbols that I would love to understand, but probably never will. It doesn’t mean I don’t have plenty to offer ecology…and I would be pretty upset if someone told me I couldn’t do what I love because I’m not a gun mathematician.

    I don’t think it helps all these “young aspiring scientists” if we continually make them pick sides – ecology/science needs mathematicians AND naturalists/intuitives (and plenty of other -ists and -icians too!). If we all belong to the same mould, how will the discipline advance at all! 🙂


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  19. I’d also like to highlight that I realized, while writing in more depth, that math-oriented ecologists SHOULD be mad at Wilson, because he was offensive in minimizing the contributions of his collaborators. He can get away with saying this shit only because he’s not planning on landing any such collaborators in the future. It’s more the icing on the cake for him, to be controversial to the end.

    • Totally agree Terry (and disagree Jim). Exactly what he really thinks about how much math he and other prospective biologists need is a little vague (or I would say inconsistent and certainly inconsistent with his actual career). But to hear Wilson tell it, Oster just applied some tools from his toolkit to record what Wilson understood. Makes it sound like Oster was a stenographer for Wilson’s brilliant insights – no value added at all.

      And Wilson never mentions what is probably his most famous piece of work/collaboration (admittedly among several really famous pieces of work) – the theory of island biogeography. There is not an iota of a chance that work would be as influential as it was if it didn’t have the mathematical development.

      To be clear, as a theoeretical ecologist with heavy mathematical training, I agree with Wilson that a lot of theoeretical ecology is puffery that is totally divorced from reality and could write a screed on that myself. (as Jeremy noted a lot of field ecology is not much better though). And as I theoretical ecologist I totally agree that biological insight is important. But Wilson goes much farther than that, specifically in the way he dismisses his collaborators and implies they are the lesser half – Wilson has insights from nature, mathematicians (who are a dime a dozen and interchangeable) have tools to record his insights. I don’t go around generically discounting the ecological insight of people in the field more than me.

      Really very arrogant and disrespectful. And to my mind makes Wilson responsible for the tone of the whole ensuing debate.

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  21. This Ted video (found through twitter) might be useful to see where Wilson is coming from. http://www.tedmed.com/talks/show?id=7321 The parts about math and scientists are almost identical to the op-ed, but I think the overall context makes them sound less outrageous. I still think the argument is wrong, though. No doubt he has a noble motive (making more young people pursue science), but his way of doing it (minimizing, almost trivializing mathematical theory as something that can easily be “contracted out” when needed) is very sadly misguided.

    In fact, in the beginning of his remarks, he starts by saying that math isn’t something to be afraid of, and any reasonably competent person can learn to do it. That is exactly what we should be saying to biology students (and everyone else, really) along with helping struggling students. But then he goes on with the stuff from the oped. More seriously, he apparently thought that the former message wasn’t the core argument, and instead kept the part that talks about how unnecessary (or easily obtained) mathematical reasoning is for the op-ed.

    On a more positive note, I think Wilson is providing a service (though in a very roundabout way, to be sure) by making us debate this issue. The loss of science majors does appear to be kind of a big deal*. But it also seems the culprit isn’t just math, and in any case, the causes appear much more complex than professors scaring away bright-eyed kids with nasty math. It would be a much more productive to discuss how we can improve instruction of math and science and also the incentive structures for specialization (driven in large part by professional school admissions). Otherwise, I think the logical conclusion of the you-don’t-really-need-math-to-do-good-science argument is this kind of idiocy: http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?src=me&ref=general

    * http://www.nytimes.com/2011/11/06/education/edlife/why-science-majors-change-their-mind-its-just-so-darn-hard.html?pagewanted=all&_r=0

  22. To various commenters here: would you be interested in a post where I talk in a really detailed way about what my various collaborations have been like? I’ve collaborated with people both more and less mathematical than me. Those collaborations came about in various ways, people brought different mixes of skills, ideas, and insights to the table, etc. I’m not sure whether such a post would be of broad interest or not, or whether most readers would just find such a post boring.

    • I think this would be valuable for all kinds of people, particularly grad students who are in labs that aren’t very collaborative. How do people initiate collaborations and how do they actually work? Some people who don’t collaborate as often as they can or should would benefit from knowing how to start and maintain one.

  23. Krugman’s quote that “the optimal amount of math for an economist to know is always, of course, exactly the amount of math you personally happen to know — anyone who knows less just doesn’t have the tools, anyone who knows more is excessively teched up” reminds me of George Carlin on drivers: “Have you ever noticed that anybody driving slower than you is an idiot, and anyone going faster than you is a maniac?”

    • Is anybody less senior than Wilson willing to say that they don’t know the math that is necessary to do what they want to do for research? I’m in that situation myself. I’m trying to find the time squirreled away to acquire the skills, but unlike Wilson, I’m not making the time to sit in on a class while in a faculty position, like he did. That in itself is a good argument that I need to sign up for a workshop or two. Collaborators are both a ladder, and a crutch, for me.

      • Well, as Brian’s pointed out in other comments, formal and informal surveys (including the response to an old post of ours: https://dynamicecology.wordpress.com/2012/10/31/what-do-you-wish-youd-learned-as-a-student-but-didnt/) indicate that most ecology students wish they knew more math and/or programming. I’d say the same–your line about collaborators being both a ladder and a crutch is spot-on in my case. It’s not so much that I can’t get by–I can. But there are a few projects I’d like to do that I’ll probably need to find a collaborator on, but that I feel like I could pursue quicker on my own, if only I had the mathematical or programming skills.

        And while your suggestion of workshops is a great one in general, the challenge of course is to find the workshops that teach the specific skills one wants to acquire.

      • Dear All,
        Thanks for the enlightening comments about those less intellectually capable than yourselves. Math does not come naturally to all, as I can attest, and hours of study is more likely to discourage further study when one finds it perplexing and often incomprehensible, certainly true in my case. I have a degree in Biology and a Masters in Conservation Biology, despite my lack of mathematical skill. I dropped maths and physics as soon as humanly possible, at 16, and yet managed to get some qualifications.

        I accept wholeheartedly that maths is a vital part of scientific endeavor, but to exclude or discourage enquiring minds because of a weak spot is the same as telling children with dyslexia that they are stupid. The number of entrepreneurs who are dyslexic or lack a formal eduction is staggering, and proves that innovation and inspiration do not require formal education.

        For those of us who are passionate about biology and natural sciences there are plenty of areas of study and hypotheses to be tested that do not require a mathematical brain to contribute to the betterment of science.

        Perhaps rather than attempting to cram every student into the same pigeon hole we should be recognizing that everyone has different skills and abilities. It already happens in every degree already as students play to their strengths and not weaknesses to get a degree. My courses, for example, had little maths in them, by choice, and E O Wilson made a significant contribution to my education all without maths.

        I would suggest that rather than taking the negative of Prof Wilson’s article we could be recognizing that the world of science would benefit from a much more open and collaborative approach to research. Indeed the world as a whole would be a better place if we all collaborated a lot more.

        Any good entrepreneur or manager accepts their weaknesses and blind spots and fills in the gaps by making use of others around them with greater expertise in those areas. Why should science be any different?

      • Marcus – either you are being deliberately provocative or its your reading skills you need to worry about!

        Nobody here said people who haven’t learned math have lower intellectual skills or anything close. Indeed its quite the opposite – pandering to the idea that some people can’t learn math that most here object to. That and the fact that Wilson more or less said that mathematical skills are up there with typing as a technical skills.

        As far the rest of your post, see my post. I don’t think you’re saying anything people here wouldn’t agree with. Except – and this is a big one – the % of students entering grad school who are “non-mathy” is way larger than the % who have strong math skills, so any idea of powers that be limiting who gets in is ridiculous. The fact that most of those non-mathy students express desires to learn more math is by far and away the best refutation of Wilson’s post.

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  27. I’m confused about the title of E.O. Wilson’s piece. The headline at the top of the article (which I assume was in the print version) reads “Great Scientist [does not equal] Good at Math” but instead of writing the phrase “does not equal” the mathematical symbol is used. But the heading at the top tab of the webpage reads “Great Scientists Don’t Need Math.” These are VASTLY different headlines and I am guessing that Wilson did not write the latter – perhaps it was put in by an editor. I apologize if someone brought this up already – I didn’t read all of the comments or even all of this post. I only noticed this after reading the very first sentence of this post. Thanks.

    • Yes Sandra, I noticed this the other day. Wasn’t sure if it was a big enough deal to be worth noting, but you’ve convinced me that I should.

      Re: the role of editors, I don’t know for sure, but it’s quite possible that editors decided both the headline of Wilson’s piece and the title on the tab of the webpage.

  28. Part of being a good scientist includes making and following logical arguments and lines of reasoning, being able to induce and deduce from premises, which I think is missing from the article. The first several points are based on creating false dichotomies and serious flawed deductions: If empiricists sometime get ideas from daydreaming, then he must mean to say the theoreticians never do and can’t? If some great scientists emphasized intuition and not math, then any scientist emphasizing math is not a great scientist. This is absurd and flawed non-reasoning. Perhaps it would behoove scientists, and the author of this piece, to take more philosophy and logic courses to avoid such flawed deductions from false dichotomies an misinterpreting the premises of Wilson’s piece.

    • Thank you for your comments Leigh. As I’ve noted in the updates, clearly there are a wide range of defensible readings of Wilson’s piece, including my reading. But whatever your feelings about my reading of Wilson (and I appreciate that you don’t agree with it, which is fine), they don’t arise from ignorance of the rules of deduction, or philosophy more broadly. I have taken a number of philosophy classes, it was one of my favorite subjects as an undergraduate. Further, Wilson’s piece is not nearly precise enough to be unambiguously understood as a series of premises from which conclusions are logically derived. I wouldn’t expect any newspaper editorial to be. Nor is my blog post, or any of the other posts on this topic, as precise as that. Precise, formal logical arguments absolutely have their place. But it’s my hope that the debate over Wilson’s piece, in my post and elsewhere, is valuable despite not being based on formal logic.

  29. Inspired by Terry McGlynn and Chris Buddle, who’ve been talking about Wilson’s piece with undergrads and high school science teachers, I’ve asked my undergrad population ecology students to read Wilson’s piece and write a page or so on their reactions. Because they’re upper-level students, I’ve also asked them to talk about how their experience in university has affected their feelings about math in science. I will share what they have to say in a follow-up post.

  30. I agree with much of what you (Jeremy) and others have written here: Math is an integral part of ecology and i doubt that in today’s world you could be successful without mathematical and statistical skills.

    However, Wilson’s article, and the subsequent discussions, also made me realize that (in my experience at least) education in ecology does not focus enough on how to develop strong questions, hypotheses, and experiments. Too often grad students spend too little time developing a strong question that will contribute significantly to the field of ecology. The large number of low impact ecological journals supports this notion (although other factors, such as the breadth of ecology, also play into the number low impact journals). Students often move forward without going through the rigorous cycle of developing ideas, reading the literature, throwing out/modifying ideas. I think this lack of education is also apparent in many younger professors. So, although I agree with the importance of mathematical and statistical skills I hope to see more focus on the fundamentals of scientific inquiry. I think graduate students/schools need to focus on both technical skills (such as mathematics) and “disciplined daydreaming.”

    • Thanks Chris.

      Re: the proliferation of low-impact journals, that’s happening in all fields. There are various reasons for it, but I don’t think they’re specific to ecology. So I don’t know that journal proliferation is a reason to worry about ecologists’ ability to develop good questions.

      I have a couple old posts aimed at students, with some advice on how to identify good questions and bad questions:



    • You’re right, that many ecologists, especially those coming out of less-than-top-notch-labs, are doing work that isn’t designed to be important even if everything worked out as great as possible. I can’t remark on other fields, but like Jeremy says, low-impact journals abound.

    • Chris,

      In my experience having a solid understanding of how statistics work (i.e. statistical skills) IS the basis for understanding scientific inquiry. I would argue that I did not know how to (really) ask a scientific question until understanding null hypotheses and type I and II errors. Can this be learned without any sort of mathematical or statistical knowledge? Yes (I think). However, for me it was a great tool in aiding that learning process.

      Also, I think that a gentle introduction into mathematical skills can open a whole new avenue to “disciplined daydreaming”, and, in fact, I would say that math (which is simply a series of logical statements) is what does the disciplining. All one must do once they understand math is to daydream.


    • Thanks Jeremy, Terry, and Paul,

      I like how you phrased it Terry: “many ecologists … are doing work that isn’t designed to be important even if everything worked out as great as possible.” This is exactly right.

      I also agree that learning math and statistics helped me learn to design good studies; however, I think there is more to asking good questions. I think asking “good” questions comes from knowing the topic area, knowing what’s been done, and being able to come up with creative, novel, and defensible (which is where I think statistics helps) ways to test hypotheses (this is easier said than done…as I’m sure I’ll learn during my PhD…so I think it needs to be taught). Indeed, having one or more hypotheses is lacking from many graduate projects. The posts Jeremy cited are excellent guidance in this regard. However, you (Paul) are right that mathematical models can help you daydream in a disciplined way, and are therefore an excellent scientific tool.

      I would argue that “the proliferation of low-impact journals, is happening in all fields” is not a good reason to suggest that we shouldn’t be concerned about it in ecology. I think we should be pushing our students and peers to be asking more important and well thought out questions that will inevitably be published in better journals (I realize I’m preaching to the choir here though). I do think low-impact journals have their place (i.e., not all studies can be earth shattering), I just think too many people strive to publish in them too often (I’m no exception). But this is off topic and has been discussed at length in other places…

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  32. I’ve been reading articles, pieces, and comments here and on Ecolog, and I wanted to throw a perspective into the ring that I haven’t yet encountered: I teach at a community college.

    Did you know that our school, in line with other community colleges across the country, place about 80% of our incoming students in developmental math? That’s not “oh, you need some practice before doing calculus” math, it’s seriously basic arithmetic and algebra. I often get students who need to take 4 courses, 2 years, before they could take calculus, assuming they pass. They have to take a full year of math before they can take chemistry.

    What’s this mean? It means I have classrooms overflowing with human service majors, education majors, business majors, and psych majors but very few science majors. I hear on a daily basis that they are in the majors/classes that they are in because they don’t get math.

    I’m on two ends of this issue. On one side, yes, we are losing potential scientists, and probably some very good ones based on students I’ve been working with, because they see the doors as completely to them due to math skills. They immediately switch into “soft” sciences, social sciences, and humanities without considering what they could be doing and if there is a way to do science without getting hung up on how long and hard math will be. With limited Pell grants and other things nowadays, those extra semesters can become cost-prohibitive quickly.

    On the other side, we’ve created a world where it’s okay to say, “I’m just bad at math” and use that as an excuse not to work your way through it and learn the skills. Now, this problem also belongs to the educators, because we can make math something that people are interested in and want to learn, but that’s going to be hard and take some creative thinking and curriculum revisiting, and folks don’t have the time, energy, and resources. I’m a huge fan of applied math. Math is everywhere and in everything, except in a math classroom where it’s a string of useless numbers and equations. I’d personally like to completely integrate math and science in our programs, which would kill many birds with few stones, but it would take collaborative teaching efforts and not many places are willing to compensate faculty well enough to try it, or their programs simply won’t allow it.

    Do I think EO Wilson had good intentions in trying to expand STEM to something that more people fell they could be a part of? Absolutely. Do I think his implementation was great? Not really. Do I hope that this conversation starts some of what we really need to get math education to be something that people want and enjoy rather than slug through hoping not to have to retake? You betcha!

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  35. I’m sure what I am about to say has been said amongst other comments, but I wanted to add my tuppence-worth. The way I read Wilson’s article, as a math-phobic ecologist, was not at all that he was implying you don’t need maths, or that you can get by without it. What I understood, and agree with, was that it shouldn’t be drilled into children, even young adults, that if they find maths hard they should just give up on the whole science idea. Surely it is better to be aware of your own weaknesses and apply the same critical, questioning, exploratory approach to your own skills that you do to your data? I know maths is not my strong point. I have to think through things slowly. Very slowly sometimes – I have to write equations out in words – to be sure that I am understanding right and applying principles correctly. Maybe someone better at maths sees this as second nature. I don’t. Surely this is good scientific practice and not, as the majority of comments above imply, some sort of horrific weakness that needs to be weeded out? Further explanation here (http://wp.me/p3iHpV-z) but I don’t think I could have been better at it earlier. So I say thank you to E.O. Wilson for bringing this discussion to light.

  36. I agree that strong math skills are hugely beneficial to ecologists, but I think the idea that you need to be strong in math to have a successful career as an ecologist is plainly false. The reason I think this is because several of the very top ecologists, as measured by their influence on the field (i.e. those with h indices > 40), have not achieved their success because of strong math skills, instead being able to influence the field by asking interesting questions, synthesising information across subfields, coming up with new conceptual models, or designing experiments eloquently so that advanced math is not required. That’s not to say that such researchers are bad at math (I wouldn’t know), but that they are not reliant on their own math skills to cut through and make an impact. The researchers I have in mind DO publish their work in journals like TREE and Ecology Letters.

    Many of these researchers collaborate with statisticians, much like what Wilson suggests, allowing them the time to focus on understanding the systems they work in; the subtleties and nuances that go unnoticed by most, which form the basis of the types of insights that simply can’t be gained by analysis alone, and are derived from intimately knowing the system you work in. Of course, that’s not to say that such insights wouldn’t be enhanced by strong math skills, merely that strong math skills are not a prerequisite to such insights.

    • “strong math skills are not a prerequisite to such insights”-> I agree it is possible, but difficult to be so sure -perhaps one should ask them!

      Some subfields like population biology are more mathematical – and for them you need strong maths skills. Certainly other subfields might have lower requirements. But to get some overview, have a look at the job market; from what I can see roughly one job over two requires both a programming background and some advanced statistical techniques.

      Also, it depends on what you mean by strong… Outside of Harvard and other fancy places, the problem is mostly that students lack the very basic tools (what is random variable, logs transform products into sums, etc.) that allow to understand the use of statistics. As said several times above.

      Moving aside from academic research, it might be a bit annoying to have wildlife managers that cannot make any sort of reliable projections of the population they study, right?

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