The past year or so has produced the resolutions of some open problems in mathematics I didn't think would be solved in my lifetime - the Jacobian conjecture, the Erdős unit distance problem, the (perhaps less well-known) Maxwell Conjecture, and most recently OpenAI's purported resolution of the Navier-Stokes existence and smoothness conjecture. This (along with Tristan Buckmaster's statement on the process leading up to this resolution) made me think it was worth organizing my thoughts on mathematics and AI. There are far more qualified people writing and thinking and talking about this (Terry Tao gave a lecture at ICM this year about math in the age of AI, and Ken Ono has been a big advocate for mathematicians implementing AI in their research), and as of writing I feel a little left in the dust - I have yet to use any LLM for anything useful research-wise.  I don't think I can say anything nebulous, like "where mathematics as a field is going to end up", but I wanted to say a few things about something more practical:

Question. As someone in their early math career, does it make sense to go all in on the AI bandwagon?

I will preface this by saying I don't give a straight answer to this question - sorry:(. In short, what I have to say is this: maybe all in is a little too far, but if you aren't incorporating AI into your work, your future career is likely in peril.

I have historically been very much on the fence about using AI at all. There are serious environmental concerns about its usage, a myriad of studies on the negative effects of AI on learning, and for a time (maybe still even now) I had my own personal feeling that using AI as an aid somehow diminishes how people will view my work. I am not even sure that this is what I truly feel. I have may colleagues who laud the power of AI, and who I deeply respect as serious mathematicians, but there is still something in the back of my mind that is telling me to pull away from its usage. Two years ago, it was as good as undergrads. Last year, it could do the work of a decent graduate students. Nowadays, it seems these models are on the level of Fields medalists, given the kinds of results that are being produced on a daily basis. So, it seems at this stage the answer to the Question is obvious, barring environmental concerns - yeah.

Yeah, but (but not really but). As someone in their early career, it is hard to know if the people on top, i.e. hiring committees for postdocs and tenure-track positions, share the same perspective. From my personal (and perhaps fragmentary) experience, opinions from the older generation are mixed. I know several tenured people in my department who actively use AI in their research, but I know just as many who share some of the prejudices I thought I carried. It is also clear to me from Tristan Buckmaster's statement that there are also likely a lot of mathematicians who prejudiced against AI for a different reason: they are wary of the danger of big companies like Anthropic and OpenAI trying to meddle in the mathematics community, and claim results "without the history intact", to put it in his words. So, if I am trying to get hired for a tenure-track position, what kind of answer to the Question should I give the hiring committee? I still think the answer here is yeah. I don't think there is any avoiding it anymore. Although one should be wary of these multi-million dollar companies having a say about what mathematics is interesting and who/what is doing it, I don't think this wariness should refute the acceptance of artificial intelligence as part of what it means to be a modern mathematician.

I want to end this essay with some incoherent half-baked rambling about the American folk hero John Henry and the Myth of Sisyphus. This nonsense might be interpreted as a weak refutation of the answer of yeah I just gave. In my ideal world, what is written below is the way things should be (in some abstract sense), but the world is unfortunately not ideal, and so one should take what is written with a grain of salt.

John Henry. It is very possible that I am just dense and was dense as a child and never understood the point of this story, so if you think what I am saying is nonsense, then it is probably safe to ignore everything else that written from here on. For the uninitiated, John Henry tells the story of a freedman working on the transcontinental railroad to the west in the mid-1800s. In the tale, he is depicted as the fastest, strongest, and generally greatest steel driver around. He is challenged to prove his skill in a race with a new technology: a steam-powered machine that does the same job. In the end, John Henry wins the race, but collapses from heart failure. To me, there is a clear analogy here to the present state of affairs, but this is really where it stops. What was the point of this story - resistance is futile? But he wins, so that can't really be it. Is the point to know your enemy? I don't really think so either. Am I stupid? Probably. Maybe if I was paying more attention in middle school language arts I'd have something more sophisticated to say. 

Sisyphus. The myth of Sisyphus (antiquity) tells the story of a man condemned by the gods to forever push a boulder up a mountain, only for it to roll down again when he gets near the top. The Myth of Sisyphus (1942) is an essay by the French philosopher Albert Camus, which introduces absurdism - it is absurd to attribute meaning to life, but one can find meaning and happiness in the search. The essay famously ends with the line: "The struggle itself toward the heights is enough to fill a mans heart. One must imagine Sisyphus happy". In less pretentious terms, doin it for the love of the game. For the purpose of this analogy, perhaps a more subject-appropriate reference is Bill Thurston's response to an undergraduate's question on MathOverflow: [paraphrased] What can I contribute to mathematics when there are people like Gauss and Euler out there? Replacing Gauss and Euler with the obvious stand-in here is essentially the point I'm trying to make, and is probably the closest to my true (but sadly, probably unrealistic) feelings on how one should approach mathematics in the modern age.

There's of a lot of very important questions I didn't address here: What does it mean to get a PhD in math now? What does it mean to teach anymore? Where is mathematics as a field going to end up? Why go to the park and fly a kite when you can just pop a pill? I don't really know, but I do think it imperative that people start talking about these things, especially at the rate things are changing.