Mathematics is Biology’s Next Microscope, Only Better; Biology is Mathematics’ Next Physics, Only Better

Intermediate Physics for Medicine and Biology is full of equations. Equations are on almost every page, and often lots of them. Russ Hobbie and I use calculus without apology, and we discuss differential equations, Fourier analysis, and vector calculus. To understand biology, must we use all this mathematics?

“Mathematics is Biology’s Next Microscope, Only Better;
Biology is Mathematics’ Next Physics, Only Better”

The answer given by Joel Cohen of Rockefeller University is Yes! In his 2004 article “Mathematics is Biology’s Next Microscope, Only Better; Biology is Mathematics’ Next Physics, Only Better” (PLoS Biol 2:e439), Cohen argues that math skills are crucial for modern biologists. He writes

Although mathematics has long been intertwined with the biological sciences, an explosive synergy between biology and mathematics seems poised to enrich and extend both fields greatly in the coming decades.

The first half of his argument I believe enthusiastically: math has much to offer biology.

Mathematics broadly interpreted is a more general microscope. It can reveal otherwise invisible worlds in all kinds of data... For example, computed tomography can reveal a cross-section of a human head from the density of X-ray beams without ever opening the head, by using the Radon transform [see Chapter 12 of IPMB] ... Charles Darwin was right when he wrote that people with an understanding “of the great leading principles of mathematics… seem to have an extra sense”... Today’s biologists increasingly recognize that appropriate mathematics can help interpret any kind of data. In this sense, mathematics is biology’s next microscope, only better.

In IPMB, Russ and I illustrate how mathematical models can describe biological and medical systems. We don’t use sophisticated or complicated math, but instead focus on toy models that train students to analyze biological problems quantitatively. On the first day of my Biological Physics class, I tell the students that the course is a workshop on applying simple mathematical models to biological phenomena. Mathematics really is biology’s next microscope.

The second half of Cohen’s argument is not as obvious. Will biology lead to new advances in mathematics?

In the coming century, biology will stimulate the creation of entirely new realms of mathematics. In this sense, biology is mathematics’ next physics, only better. Biology will stimulate fundamentally new mathematics because living nature is qualitatively more heterogeneous than non-living nature.

Well, maybe, but I am skeptical. Cohen claims that biology generates large amounts of data, and biological systems are diverse and heterogeneous, which will lead to new math concepts that deal with what we now call Big Data. I hope this is true, but I expect much of the math already exists. Perhaps my skepticism arises because I love simple models, and the new math will certainly be elaborate and abstruse. We will see.

In his article, Cohen does more than make general claims; he gives specific examples. For instance, he tells a lovely story about how simple mathematical reasoning led William Harvey to predict the existence of capillaries

[Harvey’s] theoretical prediction, based on his meticulous anatomical observations and his mathematical calculations, was spectacularly confirmed more than half a century later when Marcello Malpighi (1628–1694) saw the capillaries under a microscope. Harvey’s discovery illustrates the enormous power of simple, off-the-shelf mathematics combined with careful observation and clear reasoning. It set a high standard for all later uses of mathematics in biology.

I encourage you all to read Cohen’s article. It makes a persuasive case that books such as Intermediate Physics for Medicine and Biology are necessary and even essential. Enjoy!