The cultural divide between mathematics and AI

> Unlike many scientific fields, mathematics has no concept of "first author" or "senior author"; contributors are simply listed alphabetically.

I don't think this is (generally) true? Speaking as a math postdoc right now, at least in my field of computational mathematics there's definitely a notion of first author. Though, a note of individual contributions at the bottom of the paper is becoming more common.

> why would they be replicating it if they didn’t want it?

Who is "they"?

Most AI for math work is being done by AI researchers that are not themselves academic mathematicians (obviously there exceptions). Similarly, most AI for music and AI for visual art is being done by AI researchers that themselves are not professional musicians or artists (again, there are exceptions). This model can work fine if the AI researchers collaborate with mathematicians or artists to understand that the use of AI is actually useful in the workflow of those fields, but often that doesn't happen and there is a savior-like arrogance where AI researchers think they'll just automate those fields. Same thing happens in AI for medicine. So the reason many of those AI researchers want to do this is for the usual incentives - money and publications.

Clearly, there are commercial use cases for AI in all these fields and those may involve removing humans entirely. But in the case of art, and I (and Hardy) would argue academic math, there's a human aspect that can't be removed. Both of those approaches can exist in the world and have value but AI can't replace Van Gogh entirely. It'll automate the process of creating mass produced artwork or become a tool that human artists can use. Both of those require understanding the application domain intimately, so my point stands I think.

I had an aha moment recently. An excited AI researcher claimed, wow: claude could solve this IMO problem. Then, a mathematician pointed out a flaw which the AI researcher overlooked. The AI researcher then prompted the AI with the error and then the AI produced another proof he thought worked, but again was flawed. The AI played on the researcher's naivete.

Long story short, current AI is doing cargo-cult math - ie, going through the motions with mimicry. Experts can see through it, but excited AI hypesters are blind, and lap it up. Even alpha-geometry (with built-in theorem prover) is largely doing brute-force search of a limited axiomatized domain. This is not to say AI is not useful, just that the hype exceeds the actual.

> what it is that mathematicians want from math: that the primary aim isn't really to find out whether a result is true but why it's true.

I really wish that had been my experience taking undergrad math courses.

Instead, I remember linear algebra where the professor would prove a result by introducing an equation pulled out of thin air, plugging it in, showing that the result was true, and that was that. OK sure, the symbol manipulation proved it was true, but zero understanding of why. And when I'd ask professors about the why, I'd encounter outright hostility -- all that mattered was whether it was proven, and asking "why" was positively amateurish and unserious. It was irrelevant to the truth of a result. The same attitude prevailed when it got to quantum mechanics -- "shut up and calculate".

I know there are mathematicians who care deeply about the why, and I have to assume it's what motivates many of them. But my actual experience studying math was the polar opposite. And so I find it very surprising to hear the idea of math being described as being more interested in why than what. The way I was taught didn't just not care about the why, but seemed actively contemptuous of it.

Math-for-engineering and math-for-math courses are very different in emphasis and enthusiasm. Many engineering students tend to not care too much about proofs, so the "get it working" approach might be fine for them. Also, the math profs teaching the "math-for-engineering" courses tend to view them as a chore (which it kind of is; pure math doesn't get a lot of funding, so they have to pick up these engineering-oriented courses to grab a slice of that engineering money).