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Scary stuff from one of the winners:
"A Taxonomy of Omnicidal Futures Involving Artificial Intelligence"
(Jacob Tsimerman, Andrew Critch)
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.
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.
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.
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?
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.
Try the Quanta magazine articles.
https://www.quantamagazine.org/series/fields-and-abacus-meda...
This article explains the Kakeya Conjecture in amazing detail and understandability: https://www.quantamagazine.org/hong-wang-wins-2026-fields-me...
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?).
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.
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.
Well deserved. Congratulations to them!
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/
The winners were inadvertently announced early:
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)
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.
4 winners, 3 can speak Chinese.
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..
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.