"harmonic analysis and geometric measure theory, including applications of multiscale and decoupling techniques to the local smoothing conjecture for the planar wave equation, and major advances in Fourier restriction, Falconer distance sets, Furstenberg sets in the plane, and the Kakeya problem in three dimensions."
I'm not sure there is another profession in the world where it's impossible to explain to a layman on what the winners of their most prestigious award have worked on.
Reading the descriptions of their work makes me think of magic. It's an understanding of the principles of math and physics at a level above almost everyone on the planet - these are modern wizards.
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.
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..
- 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.
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.
"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.
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.
I don't know, maybe. I would not put Clankers on the same level (or category / level of importance) as people but if they produce the work maybe they should get the credit.
Tool-assisted proofs typically already get a description of the tool usage. Even if one wanted to start giving authorship credit to llms, they’re too non-atomic (did it have web search, which mcp?, etc.)
Not trying to delving into a deep philosophical question here but...
I asked chatgpt to write a poem about my mothers dog a while back. It spit out a poem that my mother likes and keeps around. When asked, I say chatgpt wrote it. If I asked chatgpt for a proof of the Goldbach Conjecture and it spit out a verifiable proof, I think I would go ahead and give chatgpt credit. Not that I think it is likely. It would be more of some ability (like a robot end effector is able to hold an egg) and monkeys at typewriters.
Maybe not Fields Medal worthy, but worthy of some credit.
Anything morality-related is going to be subjective, but I think there are just too many practical problems with LLMs as coauthors. For me, in a scientific context 'chatgpt' is too vague, and I think it would be logically inconsistent to have LLMs as coauthors and not other forms of Monte Carlo. I also think LLMs are just too mechanical to be ascribed 'people words' (in the same way I don't consider my automated coffee machine a barista).
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.
"harmonic analysis and geometric measure theory, including applications of multiscale and decoupling techniques to the local smoothing conjecture for the planar wave equation, and major advances in Fourier restriction, Falconer distance sets, Furstenberg sets in the plane, and the Kakeya problem in three dimensions."
I'm not sure there is another profession in the world where it's impossible to explain to a layman on what the winners of their most prestigious award have worked on.
The winners were inadvertently announced early:
https://news.ycombinator.com/item?id=48905091
One was IMO gold medal winner as well.
Reading the descriptions of their work makes me think of magic. It's an understanding of the principles of math and physics at a level above almost everyone on the planet - these are modern wizards.
Clarke’s third law.
Incredibly impotent wizards. Very little if anything they work on will have direct effects on the world.
This Fox has a longing for grapes:
He jumps, but the bunch still escapes.
So he goes away sour;
And, 'tis said, to this hour
Declares that he's no taste for grapes.
Well deserved. Congratulations to them!
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.
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..
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.
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
"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.
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.
Clankers aren't people. Should we be handing out Fields medals to LateX, python and calculators?
Do humans win Fields medals for formatting and calculation?
Python does all kinds of wondrous things
Should we be handing out Fields medal to
I don't know, maybe. I would not put Clankers on the same level (or category / level of importance) as people but if they produce the work maybe they should get the credit.
Tool-assisted proofs typically already get a description of the tool usage. Even if one wanted to start giving authorship credit to llms, they’re too non-atomic (did it have web search, which mcp?, etc.)
Not trying to delving into a deep philosophical question here but...
I asked chatgpt to write a poem about my mothers dog a while back. It spit out a poem that my mother likes and keeps around. When asked, I say chatgpt wrote it. If I asked chatgpt for a proof of the Goldbach Conjecture and it spit out a verifiable proof, I think I would go ahead and give chatgpt credit. Not that I think it is likely. It would be more of some ability (like a robot end effector is able to hold an egg) and monkeys at typewriters.
Maybe not Fields Medal worthy, but worthy of some credit.
Anything morality-related is going to be subjective, but I think there are just too many practical problems with LLMs as coauthors. For me, in a scientific context 'chatgpt' is too vague, and I think it would be logically inconsistent to have LLMs as coauthors and not other forms of Monte Carlo. I also think LLMs are just too mechanical to be ascribed 'people words' (in the same way I don't consider my automated coffee machine a barista).
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.