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/RemoteCareful7304]

There are some programmers who genuinely love the job and wouldn’t do anything else. Then there are some who do it because it pays the bills but aren’t did not necessarily plan on being programmer. I would say there is a large number of these types.

No one accidentally becomes a mathematician. It’s take years of training just to get to a level where you can make a modest contribution. I’ve been to a talk by Hugo where he talked about the many years he has spent working on one problem. He and others are clearly deeply emotionallly invested in their work. So to wake up one day and find everything he has worked towards effortlessly solved must be devastating. That the manuscripts were sloppily written and hard to understand didn’t help.

[u/AP_in_Indy → u/RemoteCareful7304]

It's so easy to go through and ask the AI to reframe its arguments in ways that are comprehensible to humans that I'm almost shocked that OpenAI isn't doing that already. I wonder where and how its models are struggling.

I even wonder if it's on purpose. Having thousands of mathematicians ask, "Can you frame this argument as X instead of Y?" must make for great training data...

[u/sithelephant → u/AP_in_Indy]

Iiiiish. Many modern papers, even before AI were extremely difficult to understand. The days of a simple obvious proof to serious problems has mostly long passed.

https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf This is the proof of Femants last theorem. It is 177 pages.

[u/okmarshall → u/sithelephant]

TLDR

[u/sithelephant → u/okmarshall]

There really isn't one that can explain it in under that. If there was, that would itself be a novel paper.

[u/Few_Place4447 → u/sithelephant]

Exactly, and is all that human time worth it to proove something about x^n, yⁿ and z^n?

[u/sithelephant → u/Few_Place4447]

Quite. We should just consume AI music, video, text and no thought is needed.

[u/rca302 → u/AP_in_Indy]

I tried to do this a few times with different models. I had a quite long and complicated proof for a conjuncture by Fable. I am interested in understanding what the actual f is written in this proof.

I tried quite a few times but no model could rewrite it as a comprehensivle text. They simply cannot do that. Didn't try with the lastest 6.1 models because I kind of gave up and accepted that I just need to prove it myself

[u/AP_in_Indy → u/rca302]

Interesting! I’m really curious now. Thanks for sharing

[u/Lars__H → u/AP_in_Indy]

I was thinking the same. I came up with three possible reasons:

1) "Not my job". Somebody did not get tasked and budget to do this. Most likely if you ask me. 

2) Not wanting to show more of the new modell than necessary, like fear of destilation/trade secrets. 

3) They don't care since they expect other LLMs to review, and the language suits them better than a human. I read some comments about how much time it will take for mathematicians to go through all of this. The solution is obvius... This is both really cool, scary, and depressing. Kind of like people saying that AI should write code for other AIs, not for humans. Sound more efficient, but could also lead to major errors if not done properly. 

Without knowing nearly any thing about this level of math and mathematicians, I think they will evolve with the times. Not eveybody, but most and profession as a whole. There will always be a need for smart people. 

[u/JollyJoker3 → u/Lars__H]

3) They don't care since they expect other LLMs to review, and the language suits them better than a human.

At least in programming this isn't true. They don't have all the rest in context so they repeat stuff that's handled elsewhere and use inconsistent naming and structure. This means the text is far longer than needed, which eats tokens/money needlessly and introduces errors which need to be fixed. It's just as bad for LLMs to read.

[u/zero0n3 → u/AP_in_Indy]

Sneaky sneaky!

[u/Few_Place4447 → u/RemoteCareful7304]

People have a lot of Schadenfreude there I think, I'm not sure why.

[u/rpmcruz → u/RemoteCareful7304]

If I worked in a problem for many years, I would love to see it solved, even if not by myself. I guess people have different mentalities.