# Key to a Fruitful Biological/Mathematical Collaboration

**BOOK REVIEW: ****Letters to a Young Scientist.** *B**y E.O. Wilson, Liveright, New York, 2013, 256 pages, $21.95.*

E.O. Wilson’s *Letters to a Young Scientist* is part memoir, part advice to young scientists. Much of the advice really does apply broadly and would be of interest to many young members of the SIAM community, with, of course, appropriate correspondences between the biological examples in the book and the interests of applied mathematicians. One of Wilson’s ideas, however, generated controversy, at least within the mathematical community, when he expressed it in an op-ed piece in *The Wall Street Journal*.** ^{1}** He seemed to be saying that scientists do not need to know mathematics. A response to Wilson’s piece appeared a few days later in

*Slate*.

**Before getting to the issue of the role and importance of mathematics, it is important to consider other parts of the book.**

^{2}What comes through in the entire volume is a sense of the importance of passion in scientific research, and of the necessity for scientists to immerse themselves in the problem at hand. These and other lessons come through clearly, in a series of specific examples from Wilson’s long life and career as an influential scientist. The advice, of course, is easily applicable to anyone who is planning on a career in research in any area of science, including applied mathematics.

Some of the more specific advice is equally applicable to scientists in a broad range of fields, and to applied mathematicians in particular. All young scientists, for example, would do well to consider the recommendation, together with specifics on how to carry it out, that they try to achieve something truly novel (called “entrepreneurship” by Wilson, as discussed in chapter 6). Doing something that is not just a publishable extension of an existing result, but rather is really new, will be more rewarding in almost all ways.

The advice about what Wilson calls “quick, easily performed experiments” applies equally to applied mathematics. Too often, the literature directed to young applied mathematicians seems to imply that results come as flashes of insight, like lightning bolts. What young readers need to understand instead is the importance of experimenting, of trying to prove a variety of conjectures—essentially, of doing precisely the mathematical equivalent of what Wilson suggests—as a way to develop really new ideas and results.

As another example, his emphasis on the importance of sustained effort comes through clearly and applies broadly. Doing research is hard work and requires looking at a problem in many different ways, just as Wilson suggests.

Now to the controversy. How does the apparent universality of Wilson’s lessons square with the part of the book in which he states that a biologist does not need to know mathematics? First, we need to look at what he actually wrote. What Wilson says is that learning mathematics was unnecessary for him because he always had someone to collaborate with. And he has made substantial contributions, as a collaborator, to theoretical advances in ecology that did involve mathematics. His suggestion is that young scientists could follow the same path and bring in the mathematics needed through collaboration. The question is, does this recipe for success still hold? Is it the best advice?

Without a recording of the interactions between Wilson and his mathematical collaborators, it is impossible to say exactly what the interactions were like. But Wilson does identify one of the most challenging and important aspects of using mathematical approaches in ecology as the formulation of the biological problem in mathematical terms, and then the interpretation of the mathematical results in the language of the biologist. This clearly requires that the biologist and the mathematician have a common language. And that is really possible only if the biologist knows at least some mathematics, and the mathematician knows some biology.

Wilson writes that the analysis of mathematical models by his mathematical collaborator did not require his input and that he did not, therefore, need to learn mathematics. I would argue, based on the need for a common language, that at least some mathematical knowledge was necessary. It might be reasonable to conclude that the greater the mathematical knowledge of the biologist, and the greater the biological knowledge of the mathematician, the more fruitful the collaboration will be. A collaboration is fruitful, after all, only when the combined knowledge of the collaborators is greater than the knowledge of any single participant. As problems become more and more complex—including, for example, those that have been the focus of Mathematics of Planet Earth—progress will require truly collaborative efforts driven by approaches across mathematics and a range of sciences. Some areas of ecology, in particular, because of the emphasis on numbers of individuals, have long required the genuine involvement of mathematicians.

A more useful rephrasing of Wilson’s advice to biologists about mathematics (and a converse statement for applied mathematicians) would be: Biologists should not be afraid to seek out mathematically adept collaborators, as advances may require novel mathematical approaches. The equally valid converse: Because advances in biology require deep biological insights, applied mathematicians should be well served by collaborations with quantitatively oriented biologists. Yet these collaborations succeed only when there is a common language, which means that all participants must work to learn as much as possible about all the fields involved.

Why is mathematics so essential for understanding biological questions? This and other challenging issues come up naturally in Wilson’s interesting memoir. I would argue that—barring distraction by the single headline-grabbing (at least for a SIAM audience) comment that studying mathematics is not important—all young scientists would greatly profit from reading and thinking about his book. And those who develop a deep understanding as to why the statement about the unimportance of mathematics is not only wrong, but essentially not supported by the arguments in the book, will find the book both more interesting and more useful.

I leave readers with a final challenge to take up after reading Wilson’s book. What would letters to a young applied mathematician (in the 21st century) look like?

** ^{1}** “Great Scientist ≠ Good at Math,” April 5, 2013.

** ^{2}** Edward Frenkel, “Don’t Listen to E.O. Wilson,” April 9, 2013.