Is math an art or a science?
I left academic math in 2007, but I still identify as a mathematician. That’s just how I think about the world, through a mathematician’s mindset, whatever that means.
Wait what does that mean? How do I characterize the mathematician’s mindset? I’ve struggled in the past to try, but a few days ago, a part of it got a little bit easier.
I was talking to my friend Matt Jones – an historian of science, actually – about the turf wars inside computer science surrounding functional versus object oriented programming. It seems like questions about which one is better or when is one more appropriate than the other have become so political that they are no longer inside the scientifically acceptable realm.
But that kind of reminded me of the turf war of the bayesian versus frequentist statisticians. Or the fresh water versus salt water economists. Or possibly the string theorists versus the non-string theorists in physics.
What’s going on in all of those fields, as best I can understand, is that different groups within the field have different assumptions about what the field may assume and what it’s trying to accomplish, and they fight over the validity of those sets of assumptions. The fights themselves, which are often emotional and brutal, expose the underlying assumptions in certain ways. Matt told me that historians often get at a fields assumptions through these wars.
Here’s the thing, though, math doesn’t have that. I’m not saying there are no turf wars at all in math, there certainly are, but they aren’t political in nature exactly. They are aesthetic.
In the context of mathematics, where nothing can be considered truly inappropriate as long as the assumptions are clear, it’s all about whether something is beautiful or important, not whether it is valid. Validity has no place in mathematics per se, which plays games with logical rules and constructs. I could go off an build a weird but internally logical universe on my own, and no mathematician would complain it’s invalid, they’d only complain it’s unimportant if it doesn’t tie back to their field and help them prove a theorem.
I claim that this turf war issue is a characterizing issue of the field of mathematics versus the other sciences, and makes it more of an art than a science.
To finish my argument I’d need to understand more about how artistic fields fight, and in particular that their internally hurled insults focus more on aesthetics than on validity, say in composition or painting. I can’t imagine it otherwise, but who knows. Readers, please chime in with evidence in either direction.