[num42]

Congrats to the winners! I’m not sure how accurate this prediction is, but 2026 may be the last time pure humans win the Fields Medal. By 2030, AI could be a coauthor on many winning results. With recent news about LLMs solving major conjectures, winning IMO gold medals, and so much rapid progress, a lot is happening.

[netvarun]

I posted a similar comment when the winners were leaked: https://news.ycombinator.com/item?id=48906573

i’d like to revise my earlier comment: 2022 may have been the last time we had pure humans win a Fields Medal.

I’m fairly certain this batch's winners used LLMs for research, lit-revews, reviewing work, and calculations... perhaps not enough to count as a co-author, but still enough to handle a lot of the grunt work.

Who would have imagined the pace of progress in LLM-powered math..

[anvuong]

It's like saying:

- winners in the 30s were the last time we have pure human to win (before computer)

- winners in the 70s were the last time we have pure human to win (before internet)

- winners in the 90s were the last time we have pure human to win (before search engine)

Why can't we treat LLMs as just another tool like computers, search engines, computing libraries? Why do people keep trying to anthropomorphizing these binaries?

People in the 1800s used to win awards and acclamation by simply hand-cranking numbers for popular calculations (Pi, error functions, etc.) and printing them in a book. This will just be the same thing.

[falcor84]

But it's not the same thing. I went through this conversation between Terry Tao and ChatGPT about the Jacobian Conjecture counterexample [0] and it looks a lot more like a conversation between peers than him using a tool.

[0] https://news.ycombinator.com/item?id=49010345

[anvuong]

Well, how many humans do you think are able to prompt this to the LLM?

"The homogeneity in x is an intertwining between a dilation (x,r,u) to (lambda x, r,u) and a dilation (P,Q,R) to (lambda^-2 P, lambda^-1 Q, lambda R) which seems to collapse the 3d jacobian to a sort of twisted 2d jacobian. Is there a general theory of such twisted jacobians and do you have any sense why those particular dilation weights were used?"

"I can see why the five-dimensional Jacobian has a nice monomial form in rho. Why does this make the three-dimensional Jacobian after restricting to c_2 = rho = 1 and eliminating the delta, eps variables also a monomial (now in x)? Is there some block-diagonal structure or something in the 5D Hessian that allows for a nice reduction? I would have expected some sort of Schur's complement type operation to appear."

I, and probably most people on here, won't be able to get the LLM to write such a detailed conversation, because we are not experts in this field. They are tools.

[bananaflag]

Read these 4 prompts and tell me again how in the future we shall still need human expertise:

https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...

[butlike]

Because the 4 prompts were actually still prompting for the original prompt (ugh.) in that the computer did not come up with a "complete unconditional counterexample" and the human expertise is required to discern that.

[ivell]

There was an article on Rudi Mandl who pestered Einstein into working on gravitational lensing.

This happened because Rudi was persistent and Einstein was kind enough.

In future, citizen scientists have a chance to work on their ideas using AI, eventhough they don't have the deep domain skills. Of course, an expert would still need to review it as usual. But it is a useful tool to democratize science further.

https://www.sciencenews.org/blog/context/amateur-who-helped-...

[falcor84]

I don't get the argument. It sounds to me like you're saying that because my own chess skills are insufficient to allow me to have a proper game with a grandmaster and I end up losing on move 10 because after a stupid blunder, then I should conclude that this grandmaster is just a tool?

[applfanboysbgon]

"Looks like" being the operative keyword there. Do you feel like you're having a conversation with a peer when you prompt an LLM in the topic you're an expert of? For the love of God, I'd hope not. The whole point is that, even though these things are really good at generating what looks like human output, they are still just regular software algorithms.

[falcor84]

> Do you feel like you're having a conversation with a peer when you prompt an LLM in the topic you're an expert of? For the love of God, I'd hope not.

Yes, I do feel that. Make of it what you will.

[applfanboysbgon]

The only thing I can think is ... how?

If I were to anthromorphize my experience with frontier models, it would be as a mentally challenged child with complete memorization of an encyclopedia and thesaurus. It has the ability to rapidly experiment and potentially succeed at tasks through trial-and-error, but not without constantly corralling it in the correct direction because it would stick a fork in an outlet if unattended for five minutes.

Tao's chat certainly doesn't give me a vibe of talking with a peer. Do you much often have conversations with colleagues where you write one sentence and then get five pages dumped on you, repeating ad infinitum? LLMs can be useful for rubber ducking, and sometimes the plausibly-related word-soup it generates so quickly will help your thinking along faster, but that's not the same thing as a genuine conversation. And it mostly looked like Tao was using it as an advanced calculator, firing off his own ideas for it to quickly do calculations on. I don't know why we need to anthromorphize these tools just because they generate sentences.

[azan_]

If you say "find some unsolved graph theory problem and counterexample for it" and LLM actually does it, is it really you that solved the problem? That's the difference vs other tools.

[fn-mote]

Is this a purely hypothetical question?

Or are you saying that’s what happened in this case. Because that’s not the way I understand it.

[azan_]

It's not, it's basically something that happened. One unsolved problem was solved with the only human input being telling LLM to work harder and to actually solve it after few failed attempts.

[mofeien]

Transcript, four prompts:

https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...

[netvarun]

https://x.com/Qiaoqiao2001/status/2080003441821163958

While there was a bunch of human effort - it is not that hard to imagine this whole pipeline becoming fully autonomous in the coming months.

[num42]

"2026 may be the last time pure humans win the Fields Medal. By 2030, AI could be a coauthor on many winning results" - netvarun

Original comment Source: https://news.ycombinator.com/item?id=48906573

Hey @netvarun, sorry about that. I originally read it in one of your comments, and I should have credited you when I mentioned it. My apologies.

There was never my intention to plagiarize. That's also why I wrote "this prediction" rather than "my prediction" but I still should have mentioned the source. My apologies again.Hope you understand.

[neaden]

What do you base that certainty on? I'm not saying you're wrong, but I am also skeptical you are correct and since it is four people you can probably look into if any of them have talked about it instead of just deciding that what you think is true.

[nl]

It's wrong - most of this work was published before 2024.

But Tsimerman in particular is very AI pilled and has talked about how he thinks LLMs will be doing better work that most mathematicians in 2 years: https://x.com/gbrl_dick/status/2080416238606717052

(He's just been hired by OpenAI)

[pmontra]

Fields medals are for humans. We can create an award for AIs for the same reason for humans and machines don't compete against each other in sports. Machines are usually faster and stronger.

[num42]

I don't remember the details exactly. I think earlier this year someone listed an LLM as a coauthor on a paper, maybe in physics or maybe another field. I remember reading about it on Reddit, but I'm not sure when or which paper it was. If anyone remembers what I'm referring to, please let me know.

[BeetleB]

> I think earlier this year someone listed an LLM as a coauthor on a paper

This is not as radical as it sounds. People did stuff like that all the time pre-LLM. It's just a question of how fussy the journal's editor is. See https://www.wired.com/2013/03/computers-and-math/ for examples in math.

HN discussion on that article: https://news.ycombinator.com/item?id=5322313