My apologies for not putting up a post last week – I hope that this will be a very occasional exception to the rule. Today, I have a really contentious topic to discuss: E. O. Wilson’s article, “Great Scientists Don’t Need Math”. I’ll start by giving my own summary of the article, and then share some thoughts on the merits of its argument.
E. O. Wilson is a well-known evolutionary biologist who’s had an illustrious career (in addition to his scientific achievements, he holds two Pulitzer Prizes for general non-fiction). The article is based on his book, “Letters to a Young Scientist”. He argues that aspiring scientists should not be discouraged from pursuing science if they feel that they lack mathematical ability, because a deep understanding of and intuition for their field can compensate for such limitations by. If needed, a scientist can always collaborate with a mathematician by explaining their intuition and asking for help in making it rigorous. Meanwhile, additional mathematical skills can always be acquired later on as necessary (Wilson gives his personal example of sitting in an undergraduate calculus class as a 32-year old Harvard professor). He concludes by saying: “For every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.”
Before I critique this argument, I’d like to note a few other people who have done so before me: Edward Frenkel on Slate, David Bailey and Jonathan Borwein at the Huffington Post, Brian McGill on Dynamic Ecology, and Jon Wilkins on his own blog (the latter critique, focusing on Wilson’s flawed interpretation of collaboration with mathematicians, is definitely worth reading if you only have time to read one more).
My first problem with Wilson’s argument is his assumption that mathematics is little more than “number-crunching”, while science is all about “concepts”. These days, the majority of data analysis is done by computer algorithms, but the ideas behind these algorithms are often as insightful as the “concepts” in science. Furthermore, mathematics not only provides a systematic way of thinking about scientific concepts, but also leads to insights that may not be obtainable directly from one’s conceptual understanding of the field. For instance, quantum mechanics, one of the great breakthroughs of 20th century physics, is notorious for its reliance on mathematics and its impenetrability to intuition, as attested by the quote by Richard Feynman: “I think I can safely say that nobody understands quantum mechanics.”
The second problem I see in Wilson’s argument is his assumption that mathematics can be learned much later on in one’s scientific career, while scientific concepts need to be learned as early as possible. In my experience, it is often much harder for biologists to learn mathematical concepts at a later stage in their career than vice versa. I’ve met a number of biology graduate students and postdocs who have asked me for help with mathematical techniques, whether for simulation, data analysis, or modeling. At the same time, several of my colleagues from graduate school have gone on to learn the skills required to perform biological experiments after getting their degree in applied mathematics, and are now successfully working in biology. In this, I agree with the late Gian-Carlo Rota, who wrote this: “When an undergraduate asks me whether he or she should major in mathematics rather than in another field that I will simply call X, my answer is the following: If you major in mathematics, you can switch to X anytime you want to, but not the other way around.”
The final part of Wilson’s argument that I take issue with is his confusion around the term “advanced mathematics”, which he uses to describe algebra and calculus. They are already a necessary part of the science undergraduate curriculum, and rightly so. Physics needs calculus for electromagnetic waves and linear algebra for quantum mechanics, chemistry relies on calculus to describe the rates of chemical reactions or the foundations of thermodynamics, and biology needs differential equations to model population dynamics – all of these are topics studied at the undergraduate level today. The social sciences are no exception, as disciplines such as psychology and sociology require knowledge of probability theory and basic statistical methods, while economics makes extensive use of game theory. With accumulating evidence that a large fraction of scientific discoveries may be erroneous, it is more important than ever for aspiring scientists to have a solid grasp of at least the basic ideas of the advanced mathematics that Wilson discusses to avoid publishing meaningless work.
There is, however, one point on which I agree with Wilson – mathematics can indeed be a “bugbear” for many aspiring scientists. The solution, however, is not the one Wilson advocates – to put off one’s mathematical education until later and focus on developing one’s scientific intuition. Instead, it is to dedicate the necessary effort as early on as possible to learning mathematics (especially the mathematics needed in one’s field of choice) so that it can pay off later. Fortunately, just like Wilson himself says, learning mathematics is similar to learning a foreign language (though, I would add, much easier because of its mostly logical structure) – a consistent effort leads to steady improvement. The real problem that we should be addressing is not reducing the need for mathematics in science, but reducing the fear of mathematics among aspiring scientists (and others), a topic that I plan to revisit later this month.