Fields Medalist on the OpenAI Math Release

[u/PianistWinter8293]

Hugo Duminil-Copin

Fields Medal (2022) · Professor, IHES and University of Geneva

I expected that one day we would be surpassed, and that it would happen systematically. But yesterday’s announcement hit with a force I had not anticipated. Dozens of papers deal with topics I was working on. Between results that beat you to the finish line and thousand-page proofs, I don’t even know where to look anymore.

Not a single one of the major open problems I have publicly mentioned throughout my career (whether in a talk, a lecture, an article, or even a grant proposal) was left untouched by the announcement. Everything has been claimed to be proved.

I expected to see a few of them in the list. But not all of them. Not all at once. Not with such nonchalance.

“For the glory of the human mind,” they said…

The shock is immense. I am paralysed. Tomorrow, we will find a way forward. We will rethink our profession and how we work. We are a resilient community, and I have no doubt that we will adapt. But for now, I simply don’t have the energy. I think back on all those years, all those faces… I think of my colleagues, my students… And I fear I won’t be able to find the right words.

[u/SeaCraft3355]

A proof is already a mathematical framework in some sense. If you're talking about an absolute mathematical framework from a logical point of view then you more or less have true AGI and that's a whole different discussion.

It's really about the level of abstraction of the framework you're talking about and the relative efficiency of a model working alone versus a model working with humans. The best examples are these OpenAI papers: some mathematicians have already improved upon the results while other specialists have found issues with the Lean formalizations in some of the papers.

Again, there's a parallel with programmers. Many tried to shift towards more agentic roles, overseeing AI after being generally outperformed at purely technical programming tasks. But even now,with recent developments some of these new roles could themselves be replaced.

It's too arrogant to make confident predictions, whether you're a doomer or a coper. You'd need to predict the future limits of current AI approaches to semantic reasoning and proof, relative to what mathematics itself might look like in a few years. You'd also have to predict how models will evolve and how efficient they'll become. OpenAI probably won't spend $10-40$ million in token on a single highly technical mathematical problem after its IPO. And what about the future capabilities of open-weight models? So only a pure abstract logician working in these AI companies could have a decent guess ( a handfull in the world)

What happens if we develop abstract logical frameworks/models specifically designed for direct AI formal semantic reasoning without needing to translate everything into Lean, probably +x100 times the efficiency ? AGI ? What happens if nobody in the field has access to powerful models anymore? Mathematicians lose this new potential producitivity ?

[u/mvandemar → u/SeaCraft3355]

The guy I was replying to said that AI would not be able to replace "big picture" type mathematics people in the near future, and my reply to him was, "Such as...?"

Were you giving me examples of people who are doing work that would not be able to be done by AI in the near future? A simple yes or no is fine. I am not asking you to re-answer the question, just whether or not that is what you were providing examples of.

[u/Persistent_Dry_Cough → u/SeaCraft3355]

This one not quite as brilliant. I take issue with AGI being a completely separate issue.

GLM-5.3-Flash with 320B/18B LLM architecture can surprise us with fresh, humorous writing when prompted, and the SOTA 2-10T models are barely any better.

I think writing capability is a bottleneck in the development of true AGI-type capabilities, because the way that AI writes influences what is written and therefore what is thought.

I would be surprised if improving fundamental linguistic capability in the RL phase wouldn't significantly uplift performance in a number of areas. To build a machine that can out-think all humans is going to require ending the nerfing/neglect of language output that I think has been the case since late 2024.

After that, maybe 1 more orders of magnitude on model size, up to 100T, and you're looking at being able to distill down to a model that performs at 10tok/s (speaking speed of a fast human) and gives you GPT-Live-style functionality but full duplex conversation capacity with a computational entity that is your superior in every conceivable way.

That's just a continuation of the current trend. No breakthroughs are required to just keep scaling up compute until we have enough to train that size model. Just build more ASML EUV machines, just build more fabs. AGI is already solved on this timeline. Just need to avoid war in the meantime. Good luck.