# Does one need math for a career in science?

E. O. Wilson has a op-ed in *WSJ* which I find quite interesting, Great Scientist ≠ Good at Math:

For many young people who aspire to be scientists, the great bugbear is mathematics. Without advanced math, how can you do serious work in the sciences? Well, I have a professional

secret to share: Many of the most successful scientists in the world today are mathematically no more than semiliterate.…

This imbalance is especially the case in biology, where factors in a real-life phenomenon are often misunderstood or never noticed in the first place. The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail.

Possibly no more than 10% have any lasting value. Only those linked solidly to knowledge of real living systems have much chance of being used.

Wilson has been on this for a bit now, to the bewilderment of some of the scientists I follow on Twitter (granted, the people I follow tend to be quantitative genomics types whose backgrounds may have been in math, physics, or statistics). Two immediate things come to mind reading this. First, **a disproportionate number of the famous and successful scientists alive today are old, like E. O. Wilson.** Just because you could get by with a certain level of mathematical fluency as an *enfant terrible* in the 1970s does not mean that that will cut it in the 2010s. Great scientists who are mathematically weak often have collaborators, post-docs, and graduate students, who do their bidding. It might be a different matter if you aren’t one of the Great Ones of the earth. From what I can tell scientists who are doing the hiring who don’t have mathematical skills prefer candidates who do have mathematical skills.

Second, a 10% success rate for formal mathematical models seems quite high to me! The vast majority of conjectures in science turn out to be garbage. If Wilson stands by the 10% figure, then that’s an argument for attaching greater value to mathematical abilities. But I suspect there is a real issue with theoretical models which haven’t been tested, or are there to simply bolster someone’s publication list (see: Journal of Theoretical Biology). In Robert Trivers’ Natural Selection and Social Theory he recounts that he was told by someone that his thinking was like that of an economist. Curiously in the same volume W. D. Hamilton advised the young Trivers to not attempt to “math up” his original ideas on reciprocal altruism so much (Trivers ignored this advice, though in hindsight he grants its wisdom). I relate this because contemporary economics does seem to have a problem where extremely powerful quantitative methods have become somewhat decoupled from the empirical questions at hand. But I don’t see that these issues are so much a problem in biology. **Rather than too little formal precision, much of evolutionary biology could benefit from greater crispness**.

At this point I have to offer that I’ve never talked to a geneticist (the people I know, who tend to be evolutionarily oriented) who has complained they took too much math. Rather, the opposite. Apparently when Theodosius Dobzhansky read papers by individuals such as Sewall Wright he would “hum” through the formal sections. Since Wilson admits up front that his math skills are not strong I feel comfortable in relaying what I’ve heard from several people associated with Harvard’s biology department: **the controversial Nowak et. al. paper which Wilson put his name to was problematic in part because Wilson likely does not grasp the formal details of the argument that he is supporting.** More concretely, E. O. Wilson has long had particular intuitions about the nature of social behavior, and he has sought out formalists who could provide him with a mathematical supporting argument. This is often how science is done, but it doesn’t seem like an optimal situation. Also, I would add that though Wilson puts the emphasis on math, perhaps just as important today is the ability to write and implement some code. Though math and programming are often connected, the rough and ready scripting which is the bread and butter of many biologists today isn’t really mathematical at all.

Of course all of this is conditional on the domain of biology one is interested in. A theoretical ecologist is going to need a lot more math than a field ecologist. Many molecular biomedical geneticists don’t have to worry about much more than standard statistical tests. And so on. But E. O. Wilson is an evolutionary biologist. Charles Darwin had great insights, and he was not a mathematical scientist. **But it is striking that a disproportionate number of Darwin’s 20th century heirs had strong mathematical orientations**. Fluency in math is not a necessary or sufficient condition for being a great evolutionary scientist. But it certainly increases the probability that you’ll have great insights which might forward the field.

**Addednum:** W. D. Hamilton was to a great extent self-taught as a population geneticist. In Nature’s Oracle Ullica Segerstrale relates that classically trained theoreticians were initially very skeptical of Hamilton’s models because they seemed rather slapdash and *ad hoc*. The reason Segerstrale explains is that Hamilton operated like an engineer, synthesizing his deep biological intuitions with a series of models, fine tuning the framework so that the theoretical superstructure was appropriately scaffolded upon the biological problem. This seems like an invitation to produce models which are not robust, but Nowak et. al. notwithstanding Hamilton’s achievements have stood the test of time.

It’s hard to do physics without being good at calculus. Not impossible, I imagine, and there’s a lot of math that isn’t required…

It’d be good if more scientists were good at statistics (which I classify as math)

wilson admits that to do physics, and much of chemistry, you need to be good at math. his focus is on biology. still not sure this is good advice even in biology. re: statistics, heartily agree. most people who use p-values probably don’t know/recall what p-values are even about. i’m thinking about a bizarre exchange on twitter that dan macarthur had about p-values and genomics with someone who was attempting to ‘school’ him and didn’t really understand that the 0.05 p-value wasn’t written in stone.

PhD student here. I wish I knew MORE math(mainly stats). And I wish I knew more scripting!!

The question, or rather, question(s) are:

1. Just how high of a mathematical knowledge should be the bare minimum required for the average “biologist” (or rather life scientist) nowadays? A decade ago I remembered it was expected standard introductory college statistics and calculus would suffice, but it seems to be much, much higher nowadays.

2. And assuming the general quantitative requirements for the life sciences are continually increasing at a substantial rate (aka computational programming as recently as a decade ago wouldn’t even been mentioned in a conversation about necessary, general skillsets vs being touted as a potential career buffer/saver these days) , are most current or aspiring biologists/life scientists capable of even gaining basic proficiency, let alone mastery, of those increasingly difficult concepts?

i don’t know if you still need to go much beyond calc and stats if you are working mostly on the bench. even if you are doing GWAS there are packages (plink) which do most of the work, and the models aren’t that crazy. if you are going more into modeling, etc., obviously linear algebra and such is going to be quite helpful.

also, it would be nice if all biologists stopped using excel and just moved to R. but i’m biased 🙂

are most current or aspiring biologists/life scientists capable of even gaining basic proficiency, let alone mastery, of those increasingly difficult concepts?i don’t think programming/scripting requires that much intelligence 😉 most scientific stuff is just-get-it-to-work, not ‘mission critical.’ as for the math, i don’t know. i think there is still going to be work for field ecologists, etc., to do. from what i can tell though purely working on the bench might be a thing of the past, as more of that gets outsourced and automated.

I think you hit the nail on the head re: programming–it’s a skill that is very useful and not very hard to grasp.

There’s also something to be said for ‘mathematical thinking.’ Understanding and doing complex mathematics is one thing, but developing good quantitative intuition is another. I found that taking courses in topics like linear algebra and formal logic and set theory to be incredibly helpful in getting me to think abstractly and analytically, even though I haven’t proved a theorem or corollary since I took those classes years ago. I would say, even you’re not mathematically inclined, a biology student could benefit from struggling through a course in higher mathematics, if only to engage intellectual muscles that don’t often get a workout in bio classes.

i don’t know if you still need to go much beyond calc and stats if you are working mostly on the benchWell, my current boss is a social scientist working in a field where things like Bayesian analysis and re-sampling methods are becoming the norm. And I’m having to explain these and other statistics topics to him from an Analysis level for him to be able to compete for funding.

So for a growing set of “bench” scientists knowing the math (and not just the equations and algorithms) is critical.

also, it would be nice if all biologists stopped using excel and just moved to R. but i’m biasedFor most sophisticated statistics and modeling the go to program is Matlab. R has been introduced to the community and discussed, but as most models are already in Matlab, it is of questionable cost effectiveness to switch.

Linear algebra is extremely useful for a quantitative geneticist, particularly for one who is interested in working on GWAS or NextGen sequence data in an intelligent manner (ie: more than just looking at additive genetic variation for a single gene at a time). It seems reasonable that if someone wants to study the missing heritability question (or just address it in their work), they should be thinking about more than just methods of examining rare variant effects, they should also be thinking about genetic architecture (ie: epistasis, haplotypes (sort of assumed in the rare variant hypothesis, but not by everyone who studies that part of the question, unfortunately), and possibly even some effects from imprinting that can be mathematically modeled). For that, you almost have to do your own programming, especially if you’ve got a complicated pedigree structure to your population.

The subtitle of Wilson’s piece talks about number-crunching and I think that goes to the heart of the matter. Being good at calculation is just one aspect of mathematical ability. At higher levels conceptualizing is more important and no one can be a good scientist who is not a good conceptualizer.

math is more conceptualizing than number crunching.

Wilson makes a similar point in his recent ‘Letters to a Young Scientist’. he adds that if you don’t have the skills, you need to partner with folks who do know their Math. He gives some examples taken from his own research projects

Is this with older scientists or with the new younger ones? or? Besides math many do not have the broad background of knowledge like the ww2 generation did many r hired in due to some connection other then being great at biology. AM surprised how much people do not know these days…do to internet addictions minds going down stream…

Wilson is of the (last?) generation where significant discoveries could be made by stamp-collecting.

If one includes formal logic as a branch of math, then he’s wrong, even about himself, most likely.

While the traditional methods of physiology have taught us much, they rely on either leaving most of the underlying processes responsible for a phenomena as black boxes or isolating part of a system. Neither approach can give us a detailed understanding of how multiple biological systems interact. Until we do have such a fine understanding, we’re left with the equivalent of sledge hammers for treating our maladies.

To really understand a system you have to be able to model it and modeling requires math.

more the latter. i’d say wright is mathy for a biologist, though he was no fisher.

“contemporary economics does seem to have a problem where extremely powerful quantitative methods have become somewhat decoupled from the empirical questions at hand.”

I don’t know much about what’s going on in the field of biology, but I’m curious if you could elaborate a bit on that part? In which way – are you thinking about classical ‘excessive formalism’? Black-boxing? Or about requirements that researchers use new and complicated methods rather than simple ones in order to get published, even though sometimes the results may be very similar? Something else?

I ask because whereas I’d wholeheartedly agree that excessive formalism is a problem in economics as a whole and that there’s a huge amount of ‘math for math’s sake’ in the field, it’s not my impression that ‘applied math’/stats for ‘applied math’/stats own sake is that much of a problem. Although ‘theoreticians’ do exist in that subfield at least my impression is that the type of people working actively with new quantitative methods tend to be very focused on actually using the methods to deal with specific problems at hand in order to better approach the empirical questions they desire to answer – they mostly seem to use the methods because they solve problems that could not otherwise be overcome. Actually the kind of people who take up actively applying new and powerful quantitative methods tend to be quite interested in doing ‘actual science’, so all else equal I’d certainly assume them to be less ‘decoupled from the empirical questions at hand” than many others in the field (like, say, the economists who don’t feel the need to deal with the messy world of real data and who thus constrain their use of mathematical methods to complicated theoretical and often untestable models. Those guys are way more likely to ‘math up’ their stuff.).

Wrt. new quantitative methods it’s important to have in mind that there’s both a question to ask regarding whether it’s appropriate to use ‘a fancy’ method, and a question to ask about how to handle the situation in case you do. Black-boxing is a major concern, so some degree of formalism is required if new methods are applied. And sometimes the ‘non-fancy’ method may simply no longer be an option, because it’s been recognized that that approach to the empirical problem is deeply flawed.

i may be unfair here. the key issue after 2008 frankly is that i got tired of hearing about the fancy math of economic modeling when it seems the field still hasn’t lived up to the aspirations of a positivistic science.

I actually have no problem understanding that sentiment and I should point out I’m hardly the only soon-to-be economist who don’t think very highly of macroeconomics. At this point I only do work at the intersection of econometrics and microeconomics – where the general approach is quite different. Most of this stuff is just applied stats on individual-level data handling questions economists might ask themselves. I know you’ve talked about twin studies before here on your blog, and I should perhaps point out that these are often used in some areas of applied micro.

You know this but it bears repeating: Economics isn’t just macro. Some other areas within economics handle the science much better.

two points

1) the social scientists who i have fruitful/productive interactions with are overwhelmingly economists. some of these are those who work at the intersection of micro and behavior genetics.

2) i think macro is a lot of hand waiving…OTOH, i recall being told pre-2008 by an eminent young economist (you’d recognize the name) that good macro is rooted in micro. i can buy that. but is this micro-rooted-macro capable of non-trivial prediction? economists are VERY smart (smarter than the average biologist). but unfortunately the topics they address aren’t so tractable….

“i think macro is a lot of hand waiving” – so do I.

“is this micro-rooted-macro capable of non-trivial prediction?” – I’ve dealt a little with that kind of micro-macro and my answer would be no. Which is part of why I’m no longer working with that stuff.

p.s. i’m generally more favorable toward econometrics fwiw….

It seems to me that a lot of the most important questions around in genetics at least are essentially abstract and quantitative in nature: we are still trying to find out how complex traits work and what we can do with the genetic information we have. Lab work is an essential part of the investigation, but you need to have statistical training to even understand some of the questions (the problem of missing heritability for example) properly.

well, questions you or i would be interested in. but there are domains of biomedical genetics where they’re still elucidating one particular mo genetic pathway. and that’s important too.

I think John McCarthy, of Lisp fame, was correct when he said those who are incapable of doing Math are doomed to failure.