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.