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.
The obvious and primary application will not be on showy millennium problems or long sought conjectures, but on optimizations and breakthroughs surrounding transformers.
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.
May all world-class mathematicians take a look at the AI alignment problem such that humanity can have a better chance of passing through, and may some of them decide to not focus just on sexy parts like coming up with ways to kill us all, and may those who do so anyway at least come up with more interesting or plausible stories than the ones presented in this paper.
I think this says more that being very good at theoretical math does not at all translate into intelligence or subject matter experience about how humans will realistically handle potential armed conflict and potential risks of mass casualties, at the political/nation-state level.
Ed Zitron should write his newsletter with LaTeX and publish them as PDFs in arxiv. Seems to make the techbros automatically take it seriously. Maybe that's what it takes to pop the bubble.
Whether or not Ed is right, he doesn't take any criticism, but peer review is a fundamental tenet of actual science. Vs being a blowhard on the Internet and getting paid for it.
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 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.
"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.
There's been some new videos uploaded with her and the rest of the prize winners (and the winners of other prizes, like the Gauss Medal): https://www.youtube.com/watch?v=mTPyjR3qmTA But after watching them I still don't think they're great for understanding (I'm still mostly confused) but the human-interest aspects of the videos are something.
Neat article. I still don't grok the Kakeya Conjecture particularly well, but thanks to the article I now understand something I never understood before, which is the idea of fractional dimensionality and what fractals have to do with it.
I used to do something similar (at a lower level), and my solution was to lie, just lie. A big part was about https://en.wikipedia.org/wiki/Wavelet_transform so my description was something like:
I work in something related to Image Compression, so when the computer has to download the image from Internet it's smaller and use less data. Anyway, I study the mathematical part, not the programming part.
The idea is that images usually have big plain parts like the sky or the wall of a house, so you use big blobs of "ink" to paint them. For the border you use smaller blobs of "ink". And very close to the border you use smaller and smaller blobs of "ink". In this method, all the blobs of "ink" has the same shape, the only difference is the size. Also, the plain parts are not perfectly plain, so you use some small blobs of "ink" there.
In a typical image, you need very few blobs of "ink" if you pick the shape of the blobs of "ink" correctly. So you can only send the position and size of the blobs of "ink", that is much smaller than sending all the information of the image. The hard part is choosing a shape of the blobs of "ink" to make this conversion automatically and very fast, without asking the computer to do something smart to select the positions.
If the listener has more technical background:
The blobs of "ink" have white "ink" in some parts and black "ink" in other parts. This correspond to positive and negative values and actually all the blobs of "ink" are an orthonormal base so the calculation is only a orthonormal base change, that is super easy and fast. There is no smart selection of the position of the blobs of "ink" positions, just a boring orthonormal base change.
If the listener has even more technical background:
Something something Fourier Transform.
I don't want to count how many lies that description has. Also, all the parts in this description were done by other persons perhaps 10 year before me. I think I only once compressed an image, just for fun, and got a tiny compression because it was a toy method (¿Haar base?).
At least you are aware of the lies. I'm reminded of Feynman's refusal to lie about the nature of magnets (https://www.youtube.com/watch?v=Q1lL-hXO27Q): "You'd soon ask me about the nature of the [rubber] bands." Even in his digression about "why" questions, in giving a very high level reason for why ice is slippery he adds "they say", since I suspect he knew at the time the usual explanation had problems, and only recently do we have better explanations (https://www.quantamagazine.org/why-is-ice-slippery-a-new-hyp...). But at the same time, I've thought, it can be fun to try and come up with nice sounding lies, or analogies, or oversimplifications, especially for some types of people who won't leave you alone about something until they think they've understood something (even if a lie), or who want something repeatable to tell their friends about so they can brag about you. Still I think honesty is a better policy, even if it's not as satisfying, and if departed from at least making sure both sides know there are convenient lies and oversimplifications. As a student I would be (and have been) very put out if the goal is to understand something on a technical level and the teacher starts with lies.
My experience talking with high level mathematicians is that they tend to know their subjects so well and are so excited to share it that they can and will scale their explanation to match their audience.
Besides the usual jargon, what I find interesting is that the tradition of always naming things after their discoverers: Fourier, Falconer, Furstenberg, Kakeya. 4 names in one sentence.
Other fields do it, but it is almost systematic in math, and arguably, it makes things even harder to understand as people names are not descriptive.
There are no way to name most problems both compactly and descriptively. The inability to attach an acceptably descriptive moniker to a problem leads to calling the problems (and solutions, theorems, etc) after the author.
But then there's the opposite in maths where there's an overload on "plain" terminology. "Normal" means a billion different things. Same as "regular" or "simple".
Omitting the human history of a field does not automatically make it easier.
IMU: We've awarded Fields medals to these outstanding mathematicians.
Hackernews: Next time it'll all be LLMs. AI's going to kill us all, though, one of the mathematicians said so! Maths is useless anyway, what a bunch of nerds. Ooh, one of them likes lesbian fanfic.
Oddly. specific. Sorry, I don't get the reference, could you please tell me what/who does that refer to (which fanfic and person, and why said person and fact is relevant to this question)
Hong Wang was the outlier among the four winners. She was not a traditional mathematical genius. She never participated in any mathematics competitions. Her major when she entered Peking University was not mathematics. During her master's studies in Paris, she even considered changing her major to study architecture.
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.
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.
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.
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.
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://news.ycombinator.com/item?id=5322313
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.
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.
The obvious and primary application will not be on showy millennium problems or long sought conjectures, but on optimizations and breakthroughs surrounding transformers.
2 replies →
[dead]
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.
they are friends according to https://www.ams.org/journals/notices/202607/noti3372/noti337...
May all world-class mathematicians take a look at the AI alignment problem such that humanity can have a better chance of passing through, and may some of them decide to not focus just on sexy parts like coming up with ways to kill us all, and may those who do so anyway at least come up with more interesting or plausible stories than the ones presented in this paper.
This is a piece of sci-fi formatted with LaTeX so it looks like philosophy.
I think this says more that being very good at theoretical math does not at all translate into intelligence or subject matter experience about how humans will realistically handle potential armed conflict and potential risks of mass casualties, at the political/nation-state level.
Just by reading the abstract it's terrifying.
Ed Zitron should write his newsletter with LaTeX and publish them as PDFs in arxiv. Seems to make the techbros automatically take it seriously. Maybe that's what it takes to pop the bubble.
Whether or not Ed is right, he doesn't take any criticism, but peer review is a fundamental tenet of actual science. Vs being a blowhard on the Internet and getting paid for it.
1 reply →
This would work better as a lesswrong post
Yu Deng is more famous now in china because he loves Lesbian fan fiction.
Can you elaborate? I don't know much about Yu Deng or lesbian fanfiction, but it's not a crossover I would have expected.
He once asked on zhihu (chinese quora) for recommendations of yuri (~= anime lesbian) fanfiction. Under his real name.
1 reply →
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.
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?
2 replies →
[flagged]
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.
2 replies →
Tsimerman's work is directly applicable in two fields of computer science: O-minimality can be used to simplify formal verification.
Username sure as hell does not check out
7 replies →
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.
6 replies →
"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.
There's been some new videos uploaded with her and the rest of the prize winners (and the winners of other prizes, like the Gauss Medal): https://www.youtube.com/watch?v=mTPyjR3qmTA But after watching them I still don't think they're great for understanding (I'm still mostly confused) but the human-interest aspects of the videos are something.
> Lysing action of the (1,2)b-carotene receptive encephalopathy pathway
High school biology is enough to get a vague idea of this though.
8 replies →
Try the Quanta magazine articles.
https://www.quantamagazine.org/series/fields-and-abacus-meda...
Quanta's video is also excellent: https://www.youtube.com/watch?v=0SNQ4HEOhSI
1 reply →
This article explains the Kakeya Conjecture in amazing detail and understandability: https://www.quantamagazine.org/hong-wang-wins-2026-fields-me...
Neat article. I still don't grok the Kakeya Conjecture particularly well, but thanks to the article I now understand something I never understood before, which is the idea of fractional dimensionality and what fractals have to do with it.
I used to do something similar (at a lower level), and my solution was to lie, just lie. A big part was about https://en.wikipedia.org/wiki/Wavelet_transform so my description was something like:
I work in something related to Image Compression, so when the computer has to download the image from Internet it's smaller and use less data. Anyway, I study the mathematical part, not the programming part.
The idea is that images usually have big plain parts like the sky or the wall of a house, so you use big blobs of "ink" to paint them. For the border you use smaller blobs of "ink". And very close to the border you use smaller and smaller blobs of "ink". In this method, all the blobs of "ink" has the same shape, the only difference is the size. Also, the plain parts are not perfectly plain, so you use some small blobs of "ink" there.
In a typical image, you need very few blobs of "ink" if you pick the shape of the blobs of "ink" correctly. So you can only send the position and size of the blobs of "ink", that is much smaller than sending all the information of the image. The hard part is choosing a shape of the blobs of "ink" to make this conversion automatically and very fast, without asking the computer to do something smart to select the positions.
If the listener has more technical background:
The blobs of "ink" have white "ink" in some parts and black "ink" in other parts. This correspond to positive and negative values and actually all the blobs of "ink" are an orthonormal base so the calculation is only a orthonormal base change, that is super easy and fast. There is no smart selection of the position of the blobs of "ink" positions, just a boring orthonormal base change.
If the listener has even more technical background:
Something something Fourier Transform.
I don't want to count how many lies that description has. Also, all the parts in this description were done by other persons perhaps 10 year before me. I think I only once compressed an image, just for fun, and got a tiny compression because it was a toy method (¿Haar base?).
At least you are aware of the lies. I'm reminded of Feynman's refusal to lie about the nature of magnets (https://www.youtube.com/watch?v=Q1lL-hXO27Q): "You'd soon ask me about the nature of the [rubber] bands." Even in his digression about "why" questions, in giving a very high level reason for why ice is slippery he adds "they say", since I suspect he knew at the time the usual explanation had problems, and only recently do we have better explanations (https://www.quantamagazine.org/why-is-ice-slippery-a-new-hyp...). But at the same time, I've thought, it can be fun to try and come up with nice sounding lies, or analogies, or oversimplifications, especially for some types of people who won't leave you alone about something until they think they've understood something (even if a lie), or who want something repeatable to tell their friends about so they can brag about you. Still I think honesty is a better policy, even if it's not as satisfying, and if departed from at least making sure both sides know there are convenient lies and oversimplifications. As a student I would be (and have been) very put out if the goal is to understand something on a technical level and the teacher starts with lies.
1 reply →
My experience talking with high level mathematicians is that they tend to know their subjects so well and are so excited to share it that they can and will scale their explanation to match their audience.
I mean, they likely have practice!
Dating or maybe a significant other, parents, siblings, any BBQ event IE any social event outside academia where someone asks "So what do you do?"
1 reply →
Besides the usual jargon, what I find interesting is that the tradition of always naming things after their discoverers: Fourier, Falconer, Furstenberg, Kakeya. 4 names in one sentence.
Other fields do it, but it is almost systematic in math, and arguably, it makes things even harder to understand as people names are not descriptive.
There are no way to name most problems both compactly and descriptively. The inability to attach an acceptably descriptive moniker to a problem leads to calling the problems (and solutions, theorems, etc) after the author.
But then there's the opposite in maths where there's an overload on "plain" terminology. "Normal" means a billion different things. Same as "regular" or "simple".
Omitting the human history of a field does not automatically make it easier.
Mathematicians might be good with math but their naming skills is atrocious
Same with their ability to summarize and explain things
And their ability to create mathematical objects that are similar, but weird in a funky way, to the actual real objects.
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!
The winners were inadvertently announced early:
https://news.ycombinator.com/item?id=48905091
IMU: We've awarded Fields medals to these outstanding mathematicians.
Hackernews: Next time it'll all be LLMs. AI's going to kill us all, though, one of the mathematicians said so! Maths is useless anyway, what a bunch of nerds. Ooh, one of them likes lesbian fanfic.
> Ooh, one of them likes lesbian fanfic
Oddly. specific. Sorry, I don't get the reference, could you please tell me what/who does that refer to (which fanfic and person, and why said person and fact is relevant to this question)
It was a reference to https://news.ycombinator.com/item?id=49031519. Not a topic I know anything about.
1 reply →
The quote I've seen was that Yu Deng dedicated part of his success to reading yuri (lesbian themed) manga.
Hong Wang was the outlier among the four winners. She was not a traditional mathematical genius. She never participated in any mathematics competitions. Her major when she entered Peking University was not mathematics. During her master's studies in Paris, she even considered changing her major to study architecture.
[flagged]
4 winners, 3 can speak Chinese.
[dead]
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.
17 replies →
"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.
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.
1 reply →
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.
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://news.ycombinator.com/item?id=5322313
[flagged]
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.
3 replies →
Do humans win Fields medals for formatting and calculation?
1 reply →
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.
4 replies →