How much math(s) and stats should undergraduate biologists learn? And at what opportunity cost?

To give a quick bit of context for any non-American readers: at American universities, over the course of a four-year degree, a student typically takes approximately 1/3 of their coursework within their "major" (degree concentration, in this case some flavor of ecology and evolutionary biology), 1/3 of their coursework on what is often called "distribution requirements" (classes spread out over many different disciplines or skill sets, e.g., humanities, social sciences, STEM, writing-intensive, foreign languages), and 1/3 on electives (advanced coursework within the major, adding a second major, courses for fun in other disciplines, etc). Americans generally don't apply to do a particular major -- they apply to the university itself, and then during their first or second year they declare which major they're going to be.

I did my undergraduate degree at Yale, where I double-majored in Mathematics and Ecology & Evolutionary Biology (EEB). At the time, the EEB degree required two semesters of calculus and one semester of statistics, though you could place out of the organic chemistry requirement if you took two or more advanced mathematics courses. (I actually really enjoyed my intro to chemistry course, but I was already petitioning the Committee on Honors and Academic Standing nearly every semester for special permission to take a greater-than-normal courseload -- orgo just didn't make the cut.) Anyway, that was it for required quantitative training, though you were highly encouraged to seek out more.

As a math major, I had coursework in multivariate calculus, linear algebra, real analysis, group theory, set theory, game theory, graph theory, and both theoretical and applied probability and statistics; I did my math senior thesis on representation theory and Fourier analysis. (Yes, I'm missing complex analysis -- I decided to take a class on macroevolution that met at the same time. Yes, that's why I have honors in EEB but not in math. Give that I now have a PhD in, esssentially, macroevolution, it was the right call.) As a teenager, I attended Canada/USA Mathcamp, so I also have all sorts of random knowledge of topics that I studied there, like cryptography and number theory.

Some of these topics that I just listed are

Moreover, numbers don't scare me. Logic doesn't scare me. Programming doesn't scare me. Even if I'm never, ever going to need to prove that a 17-gon can be constructed with a ruler and compass (something that comes up towards the end of an undergraduate Galois Theory class), I'm grateful for the rigorous mental training that a mathematical education provided. I'm grateful that I have enough of a mathematical education that I can teach myself anything else that I need to know to do my job as a biologist.

Should all ecologists double-major in mathematics? No, of course not. But every single biologist I know wishes that she knew more stats, myself included. And if you're going to go beyond first-semester stats, you're going to need to know basic calculus, which is where this whole debate started.

So why is statement this controversial? I think this is controversial because in higher education, mathematics, statistics, and programming are often taught to too general an audience. (And also by people who aren't trained to teach and/or by people who aren't incentivized to be effective teachers, but oh boy is that a can of worms I'm not touching.)

So what do we do? We design classes specifically for the biological sciences. The type of mathematics you need to know if you're going to be an physicist is very different from the type of mathematics you need to know if you're going to be an ornithologist. We also know our audience -- teaching stats to someone who did A-level Further Maths (UK) or who is considering a math major (US) is very different from teaching stats to someone who shuts down at the sight of arithmetic. Teaching R to someone who's fluent in Python is very different than teaching R to someone who has been told all of their life that people from their minority group "can't code." All of these factors have to be worked into the framework of the class itself, though if we as individuals have no control over the syllabus, we do our best with what we have.

There are many different ways to be a "biologist." But every single one of us applies the scientific method. Which means testing a hypothesis. Which means using statistics. Which is a type of mathematics. A poorly-taught mathematics class is a waste of an undergraduate's time, sure, but I think that we can do better than that.

How much mathematics should an undergraduate learn? At least some, preferably well-taught. Enough to build their confidence. Enough to show them that numbers aren't scary. Enough so that when they have to learn more, they can teach themselves.

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