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.
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.
"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 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.
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.
Peer review is actually a surprisingly modern concept. It is not actually a fundamental tenant of science. The scientific method notably doesn't actually include peer review in it's core.
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.
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.
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.
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.
21 comments
[ 1.4 ms ] story [ 23.2 ms ] threadhttps://news.ycombinator.com/item?id=48905091
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.
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.
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?).
"A Taxonomy of Omnicidal Futures Involving Artificial Intelligence"
(Jacob Tsimerman, Andrew Critch)
https://arxiv.org/pdf/2507.09369
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.