Jellymatter is, we claim, not afraid of equations, but apparently scientists are. A study in PNAS claims to have found that theoretical biology papers are cited less when they are densely packed with mathematical language. The authors argue that this impedes progress, since empirical work needs to be backed up and commensurate with some theory to have deeper scientific meaning.
I think it’s a very interesting point. Mathematics is often said to be the language of science, but actually, contrary to perceptions that many people might have, most scientists aren’t big fans of maths. But using maths is one of the ways that scientists try to make the meaning of their work precise – without it, scientific theory is too vague and subject to interpretation. In that way, maths should be an aid rather than a hindrance to communication.
Maths also gives you a way to be sure of what logically follows from the statements you make. As a simple example, think of the simultaneous equations you learn in school – if you are given that x+y=2, and x-y=0, you can show that as a logical consequence of these assumptions x and y must both themselves be equal to 1. Much of the use of maths in scientific theory comes down to derivations like this, and it allows you to be sure that your results follow logically from your propositions.
Yet in spite of its advantages, it seems maths turns off a lot of scientists. Actually probably the most influential work in theoretical biology, Darwin’s On the origin of species, contains essentially no maths. By contrast, I’ve recently been reading Norbert Wiener’s Cybernetics, which is again an influential work, but it relies on a lot of maths, and I wonder if perhaps this puts people off really appreciating Wiener’s arguments.
Finally, at the end of the story on this paper here, one of the authors is quoted arguing that maybe a good middle way is not to exclude maths from theoretical work, but to make sure to add more explanatory text. This is clearly a sensible suggestion. We also perhaps shouldn’t generalise too much – maybe maths does put off some scientists, but as I have pointed out, it also has some strong advantages. While highly mathematical papers might not be the most popular or influential, they do still have a place and a utility.