I'm a PhD student working in probability and analysis, and right now the problem I'm working on could be considered a moderate extension of some existing theory. But it seems like AI is leading to the rapid devaluation of such work and pure "problem solving" as a skill in general (see for example https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy ). If i were to summarize with an analogy - the stock of combinatorialists feels like it is falling while that of people working on geometric Langlands feels like it is rising.
The common sentiment pretty much everywhere seems to be that mathematicians will now be AI guiders and checkers (although the status quo is changing quite literally every day), and those with a wide vision of the entire mathematical "forest" will survive and those who "solve problems for the sake of solving problems" will not or at least will be deprioritized. Honestly, when I think about it, the problem I am working on is small enough in scope that it could probably just be plugged into ChatGPT Pro and solved after some thinking by the model, with no input of my own except a decent prompt. And I have a subscription to GPT Pro, but I still struggle to do that because it just feels so pointless. But at the same time, I feel pointless and obsolete, because - well I am, because my core skillset is problem solving.
Everywhere I look, I see posts stating something to the effect of "solving problems is not the point of mathematics, improving understanding is". And I kind of get it, it's a little evidenced by the counterexample to the Jacobian conjecture, which I saw, and basically said - ok cool, now what? But on the other end, as someone who enjoys struggling with a problem (without thinking about any broader implications), that aspect of math disappearing is deflating. As Paul Halmos famously said:
"Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"
Sorry, this turned into a rant, but I assume many others are struggling with this transition and I wanted to just get a consensus and some opinions of what people are doing or think is the right thing to do, other than just quit and start feeding questions to AI and become AI guiders. Because if that's what math is going to become, I'd rather not do it and just pursue another field. Literally today, I found a paper on the Arxiv which literally set up a system to autonomously dig through arxiv papers for open problems and then feed them to some kind of LLM to see if it can prove it. Sure, this kind of activity is seeking truth and trying to advance the frontiers of mathematical knowledge - but is this really the point of math? Is this really what it's all about and what it's all going to be?
Here's an example of a non-specialist proving a result which is true just by plopping it into an LLM - it is literally "vibe math":
https://x.com/vikvang1/status/2079370200286433340
The example below is by people who are experts in the field, but basically created an autonomous system to trawl papers for open problems and then feed them into LLMs so that they can find solutions. Big caveat here: I have a lot of respect for the authors - they discuss the impacts of AI in terms of dislocation of early career researchers, and the general societal impacts and how humans are still important. I laud them for that. But still, it's ultimately an automated system to find problems and solve them, almost for the sake of solving them.
https://arxiv.org/html/2607.17388v1
What is the point of working on specialized/non-famous problems and understanding a field deeply if this is what's happening now?