"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.
I bet she could do it. Maybe not in a sentence, but at least the Kakeya problem is easy to understand, so maybe these other things would be explainable by an expert. I would like to see them try at least!
fwiw, I feel the same way about biology "Lysing action of the (1,2)b-carotene receptive encephalopathy pathway" type shit.
Jacob Tsimerman believes that AI will be better than human mathematicians within 2 years.
We should not be surprised if AI solves the Millenium problems very soon and advances to a level that is barely comprehensible, or even incomprehensible, to the best humans.
We can expect this not by curve fitting to recent progress but by reasoning from first principles about where the progress has come from (synthetic data, non-human corpus) that has no obvious upper bound on capabilities.
Does anyone know if Tsimerman talked about AI extinction risk at other places? Critch has worked long-term in the field (MIRI, CHAI) but I was surprised to see this colab.
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.
So now the Emperor walked under his high canopy in the midst of the procession, through the streets of his capital; and all the people standing by, and those at the windows, cried out, "Oh! How beautiful are our Emperor's new clothes! What a magnificent train there is to the mantle; and how gracefully the scarf hangs!" in short, no one would allow that he could not see these much-admired clothes; because, in doing so, he would have declared himself either a simpleton or unfit for his office. Certainly, none of the Emperor's various suits, had ever made so great an impression, as these invisible ones.
"But the Emperor has nothing at all on!" said a little child.
"Listen to the voice of innocence!" exclaimed his father; and what the child had said was whispered from one to another.
"But he has nothing at all on!" at last cried out all the people. The Emperor was vexed, for he knew that the people were right; but he thought the procession must go on now! And the lords of the bedchamber took greater pains than ever, to appear holding up a train, although, in reality, there was no train to hold.
So overhyped. Yet they have no power but some prestige among nerds. The reason why it is bad is that the money/status is very limited relative to the amount of smart people. I would rather praise developments in quantitative sciences.
Not true. Novel mathematical methods precede their application by at least a decade and widespread use by about a century.
Calculus was invented in 1670, it was about 1680-1700 till it started actually being used in astronomy. The uptake was probably faster because at that time a lot of mathematicians were Astronomers as well.
There is a lot of mathematics created but we don’t yet know how to use it. My hope is that AI can bridge the search gap to accelerate this.
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.
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.
We know which bots are the best at Chess. You'd care which AI is the most accurate at diagnosing your medical condition. It's not a bad thing to keep track of which automated systems are the best at certain tasks.
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.
> 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.
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.
> 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.
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.
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.
"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.
I bet she could do it. Maybe not in a sentence, but at least the Kakeya problem is easy to understand, so maybe these other things would be explainable by an expert. I would like to see them try at least!
fwiw, I feel the same way about biology "Lysing action of the (1,2)b-carotene receptive encephalopathy pathway" type shit.
Try the Quanta magazine articles.
https://www.quantamagazine.org/series/fields-and-abacus-meda...
The winners were inadvertently announced early:
https://news.ycombinator.com/item?id=48905091
Scary stuff from one of the winners:
"A Taxonomy of Omnicidal Futures Involving Artificial Intelligence"
(Jacob Tsimerman, Andrew Critch)
https://arxiv.org/pdf/2507.09369
Jacob Tsimerman believes that AI will be better than human mathematicians within 2 years.
We should not be surprised if AI solves the Millenium problems very soon and advances to a level that is barely comprehensible, or even incomprehensible, to the best humans.
We can expect this not by curve fitting to recent progress but by reasoning from first principles about where the progress has come from (synthetic data, non-human corpus) that has no obvious upper bound on capabilities.
Does anyone know if Tsimerman talked about AI extinction risk at other places? Critch has worked long-term in the field (MIRI, CHAI) but I was surprised to see this colab.
This is a piece of sci-fi formatted with LaTeX so it looks like philosophy.
Just by reading the abstract it's terrifying.
One was IMO gold medal winner as well.
*Two IMO gold medal winners. Three ISO gold medal winners. Six ISO gold medals collectively :)
- Yu Deng: IMO gold [1]
- Jacob Tsimerman: 2x IMO gold [2]
- John Pardon: 3x IOI gold [3]
Fun fact: Tsimerman and Deng both overlapped with Peter Scholze (another Fields Medal recipient) at the IMO
[1] https://www.imo-official.org/results/contestant/8824/
[2] https://www.imo-official.org/results/contestant/7387/
[3] https://stats.ioinformatics.org/people/1141
Well deserved. Congratulations to them!
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.
The description of Yu Deng's work should be accessible to someone who's taken condensed matter physics in grad school.
Is this supposed to imply that it's accessible?
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.
So now the Emperor walked under his high canopy in the midst of the procession, through the streets of his capital; and all the people standing by, and those at the windows, cried out, "Oh! How beautiful are our Emperor's new clothes! What a magnificent train there is to the mantle; and how gracefully the scarf hangs!" in short, no one would allow that he could not see these much-admired clothes; because, in doing so, he would have declared himself either a simpleton or unfit for his office. Certainly, none of the Emperor's various suits, had ever made so great an impression, as these invisible ones.
"But the Emperor has nothing at all on!" said a little child.
"Listen to the voice of innocence!" exclaimed his father; and what the child had said was whispered from one to another.
"But he has nothing at all on!" at last cried out all the people. The Emperor was vexed, for he knew that the people were right; but he thought the procession must go on now! And the lords of the bedchamber took greater pains than ever, to appear holding up a train, although, in reality, there was no train to hold.
The fox who longed for grapes, beholds with pain
The tempting clusters were too high to gain;
Grieved in his heart he forced a careless smile,
And cried, 'They’re sharp and hardly worth my while.'
So overhyped. Yet they have no power but some prestige among nerds. The reason why it is bad is that the money/status is very limited relative to the amount of smart people. I would rather praise developments in quantitative sciences.
Not true. Novel mathematical methods precede their application by at least a decade and widespread use by about a century.
Calculus was invented in 1670, it was about 1680-1700 till it started actually being used in astronomy. The uptake was probably faster because at that time a lot of mathematicians were Astronomers as well.
There is a lot of mathematics created but we don’t yet know how to use it. My hope is that AI can bridge the search gap to accelerate this.
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.
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.
Clankers aren't people. Should we be handing out Fields medals to LateX, python and calculators?
We know which bots are the best at Chess. You'd care which AI is the most accurate at diagnosing your medical condition. It's not a bad thing to keep track of which automated systems are the best at certain tasks.
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.
> but if they produce the work maybe they should get the credit
But that's not what the Fields Medal is for.
If you're a 41 year old mathematician and do amazing groundbreaking world shifting math, you can't get a Fields Medal either.
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.
> 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
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.
> 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.
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.
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.
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.
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.