A mathematician's perspective

As a math PhD student, I've been having a number of alarming conversations with my colleagues, none of which came to any concrete conclusion. I'm interested in some different takes, so for what it's worth I'll just share my thoughts and the thoughts of some of my colleagues.

About me:

- I started my PhD in February

- It is in mathematical physics

- I'm not an AI die hard crank nor am I completely anti AI

Scenarios for future maths research

Scenario #1: this moment right now is just the initial shock, AI is going to improve but as it finishes the human material for its training it's going to reach a plateau in terms of the quality of its output. At that point, when the dust settles, us mathematicians will learn to rely on its improved capabilities, publish more human-written papers, train the AI on those, then catch up and so on in a sort of tidal-wave dynamic. I think this is the most likely scenario honestly: if AI starts to train on its own material, which regardless of its correctness is exposed usually very very badly, its output is bound to get worse.

But I know yall don't believe in this, this is r/singularity after all. So let's move on

-Edit: lots of people got hung up on this, maybe they're right, I honestly don't know enough about the training process to tell if the data is going to be the bottleneck at some point. I just thought that if initial data can get you to some point, better initial data can get you further, so assuming there's an end then it needs to be related to the quality of the initial data. Is there an end? Well, nobody currently knows, but I really have to think that the answer is yes and that at some point we necessarily will have some kind of big bottleneck. This level of growth can't continue forever, just look at how Moore's law played out. If it slows down enough, whatever point it will have reached, I have faith that we will adapt and catch up and be able to do maths using this new tool.

Scenario #2: let's just pretend that AI becomes so good that it basically becomes an unknowable mathematics oracle. Is there still a role for mathematicians in this world?

Here's my take: mathematics has always been a completely masturbatory endeavor. It is something we only do out of curiosity. Until now we've always been able to get some funding because we've been hiding behind the fact that yeah this theorem is completely useless now, but 150 years down the line some physicist is going to try to model something that needs exactly that and so we contribute to science and the well-being of humanity, that's how maths departments make the case for getting their taxpayer money.

I've always seen a lot of hypocrisy in this. When people used to talk about the Navier-Stokes problem in a public lecture, it was always described as important because fluids are central in engineering and planes and shit.

The Navier-Stokes problem was completely 100% useless for any kind of application. We've always known that. It is a mathematical masturbatory question about convergence of a PDE. Now that it has been solved by AI though, suddenly everyone had a sudden surge of honesty and admitted that it's completely useless, just to downplay the size of this result.

This is bad communication and it's the reason I absolutely despise public lectures. They're lies made up to sell you a product - in this case, a mathematics course at your uni.

-Edit: I don't want you to misunderstand: it is absolutely true that often what physicists or scientists need is (some - not all) mathematical structures that were invented decades earlier. I'm just arguing that that's not what maths research is about.

This is true for theoretical physics too mind you.

Application is not what anyone is in (pure) maths for, and I say that as I'm doing my PhD in mathematical physics and string theory.

If in this hypothetical future the physicists get their hands on this mathematical oracle that can suddenly out of nowhere tell them what is the mathematical structure that models that specific phenomenon, then our excuse for getting funded disappears, and that is everyone's worry at the moment.

As a community, our main task right now is to be introspective and ask ourselves why it is that we do maths in the first place, and do it honestly, not just finding talking points to get grants. I have my own personal answer as to why I do maths, everyone does, but there is no community level answer, and I think that's the main issue. Once we figure that out, we can ask ourselves whether AI really undermines that.

I see this scenario becoming real only if somehow the AI becomes much better at mathematical exposition. I've heard some might argue that simplifying an argument to get good exposition shows an understanding of a sense of "elegance" and clarity that the AI cannot develop. I don't buy this argument, I think it's a huge cope, but my gut feeling is still that tech just can't improve forever and some kind of plateau (whether it's computing power or something architectural like having enough high quality data anymore or something else) has to manifest itself at some point.

About Terry Tao's post (edit - apparently this is not Terry's take, it was a repost of someone else's opinion. Everything I say here is about the author, not necessarily Terry)

I hate his take. I'm a mathematician and he doesn't speak for me. I think it is completely hypocritical to say "mathematicians didn't ask you to do this". Maths is for everyone, and in particular it must be for OpenAI too. It's an absolutely hideous opinion that exemplifies everything that I find bad and fake about this community, and he should feel ashamed for having said that so openly.

That said, the way OpenAI handled this was also very bad.

For one, there's the usual issue of not citing the relevant literature, which is IP theft, but AI companies are not new to this kind of shitty behavior so I shouldn't be surprised.