alt Hacker NewsThere's a long collection of comments by mathematicians at [1]. A large number of workers in the field are rather discouraged. The main quality complaint is that the proofs are ugly, long, and incomprehensible. One mathematician comments that the first proofs of new major results are often like that. Elegance comes later. The main social complaint is that the social foundations of mathematics just changed, in a big way. The main practical complaint is "what do I do now", especially from PhD students who just lost their thesis topic. They sound like the Uber drivers fighting Waymo.
One comment was "A common piece of wisdom is that mathematicians only have a few tricks in their bag – which they skillfully apply again and again." Feynman made that point in his autobiography. For various reasons, he had a different set of mathematical tools than others in his field, and that helped him to solve problems that stumped others.
A big AI model has access to all known tools. AIs have more breadth than any human. Some of these breakthrough proofs seem to come from applying techniques from areas different from what people in the field tend to use. I'm not qualified to comment on math at that level, but the comments by mathematicians seem to hint in that direction. That may indicate why throwing vast amounts of compute at these problems works - an AI can try everything.
[1] https://proofsandprompts.com/2026/10/08/100-reactions-to-100...
Replies
Not only are the proofs long and unintelligent, but they don't cite previous work.
In fact, they completely disregard all standards of mathematical dissemination. They just post a bunch of 100+ page papers online and call it the day.
A real mathematician polishes and polishes for months until it is understandable by the community. Then they communicate the results to a journal where there are editors and peer reviewers who come with detailed feedback which is then implemented. And just then it is ready to publish.
> The main practical complaint is "what do I do now", especially from PhD students who just lost their thesis topic. They sound like the Uber drivers fighting Waymo.
I wish mathematicians would just focus on this. This really is the problem, at the end of the day.
Having models get better at writing elegant proofs and explaining their results will not solve this problem - it will only make it worse, if anything.
We are all sympathetic to this. I, personally, am much less sympathetic to the absurd notion that it is "bad" that this new technology can solve important open mathematical problems at all, that we should stop trying to solve them, that things like the Mathathon are dangerous and needs to be shut down, that ugly proofs are the real problem here, so much so that you wish the open question weren't resolved at all, and so on. So silly.
But being pissed off that people are going to be out of work is something I agree 100% on. Hopefully, much like the internet, there's a way to make the whole thing a net benefit for society.
> The main quality complaint is that the proofs are ugly, long, and incomprehensible.
Let's take an example: Maxwell's 1865 paper states electromagnetism as 20 equations in 20 unknowns, written out in components. His 1873 Treatise recasts parts of it in quaternions, which was even more esoteric. The four vector equations everyone learns are Heaviside's, from 1884-85, five years after Maxwell died. The clean form came from other people working on the ugly original. Had Maxwell waited until he had something elegant, it would have been a net negative to society. Yes there was cleanup but I would argue that's a part of learning and understanding.
I think part of this mentality is a perfectionists view that does not always align with our "messy" reality.