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
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.
Then, I don't see the value in dropping 700 results 500 of which were just low hanging fruits waiting for a PhD student to solve. That is just being a bully for the purpose of showing that the AI's raw throughput is more than that of a human, and I don't think anyone needed proof of that. Until we completely reform the way PhD's are handled, there is really no point in doing these sorts of stunts, this is just eating our work. The results are not hard not prestigious, we use these low hanging problems just to build the bones of future researchers.
Also, most of them are unchecked and literally the day after release people already found mistakes in the proofs using Astra. They couldn't even be bothered to ask Astra to check the results, and that just shows how much they care about the maths itself: it's clear that no human has actually read through all the slop. Clearly this can't be the future of research.
I actually buy the case for the Lean-formalized bigger results like the quasi-Riemann hypothesis. I think it's incredibly sick, but again a human will have to go through the results to check that actually the lean code is reflecting the natural language paper, which is not guaranteed.
If they had only released the 100 biggest papers but had put any care in writing and formalizing them, I don't think anyone would have any sensible reason to criticize them, and I myself would just dismiss the mathematicians' response as just being emotional. They would've still have made headlines and I would've been all for it, while by doing this stunt they just gave talking points to the haters. This is not how we (or anyone, including AI) should do research.
There's one last thing I want to point out: regardless of which scenario plays out, this tech is here to stay, and we should not pretend otherwise. We should all adapt to use it in our day to day research. However, to me it is really uncomfortable to give all this power to a private company. In a perfect world, AI is completely nationalized and instead of stealing IP we all contribute to it in a transparent and institutionalized process. Now, I'm not naive, I know this is not how things will play out in the short term, but it's really the only reason why even I feel a bit of an ick when I use the codex for my own research. I don't want all research to only become prerogative of whoever happens to have the computing power, that is a very dangerous slippery slope towards a cyberpunk dystopia.
I'm curious to hear other takes on this. I'm very disappointed by the maths community response, I really hoped that we would react better than the artists, but in the end it turns out we're all human. At the same time, I think OpenAI should've handled this differently. Overall, I'm stoked about the tech, but I'd much prefer it if they had someone who actually gave a shit about maths running this research.
Also I should mention that I really don't buy their figure of "3 hours of chatGPT pro", I think that's all marketing.