How much math do scientists need to know?
I’m catching up with reading the “big data news” this morning (via Gil Press) and I came across this essay by E. O. Wilson called “Great Scientist ≠ Good at Math”. In it, he argues that most of the successful scientists he knows aren’t good at math, and he doesn’t see why people get discouraged from being scientists just because they suck at math.
Here’s an important excerpt from the essay:
Over the years, I have co-written many papers with mathematicians and statisticians, so I can offer the following principle with confidence. Call it Wilson’s Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.
Given that he’s written many papers with mathematicians and statisticians, then, he is not claiming that math itself is not part of great science, just that he hasn’t been the one that supplied the mathy bits. I think this is really key.
And it resonates with me: I’ve often said that the cool thing about working on a data science team in industry, for example, is that different people bring different skills to the table. I might be an expert on some machine learning algorithms, while someone else will be a domain expert. The problem requires both skill sets, and perhaps no one person has all that knowledge. Teamwork kinda rocks.
Another thing he exposes with Wilson’s Principle No. 1, though, which doesn’t resonate with me, is a general lack of understanding of what mathematicians are actually trying to accomplish with “their equations”.
It is a common enough misconception to think of the quant as a guy with a bunch of tools but no understanding or creativity. I’ve complained about that before on this blog. But when it comes to professional mathematicians, presumably including his co-authors, a prominent scientist such as Wilson should realize that they are doing creative things inside the realm of mathematics simply for the sake of understanding mathematics.
Mathematicians, as a group, are not sitting around wishing someone could “make use of their equations.” For one thing, they often don’t even think about equations. And for another, they often think about abstract structures with no goal whatsoever of connecting it back to, say, how ants live in colonies. And that’s cool and beautiful too, and it’s not a failure of the system. That’s just math.
I’m not saying it wouldn’t be fun for mathematicians to spend more time thinking about applied science. I think it would be fun for them, actually. Moreover, as the next few years and decades unfold, we might very well see a large-scale shrinkage in math departments and basic research money, which could force the issue.
And, to be fair, there are probably some actual examples of mathy-statsy people who are thinking about equations that are supposed to relate to the real world but don’t. Those guys should learn to be better communicators and pair up with colleagues who have great data. In my experience, this is not a typical situation.
One last thing. The danger in ignoring the math yourself, if you’re a scientist, is that you probably aren’t that great at knowing the difference between someone who really knows math and someone who can throw around terminology. You can’t catch charlatans, in other words. And, given that scientists do need real math and statistics to do their research, this can be a huge problem if your work ends up being meaningless because your team got the math wrong.