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Fields Medals 2026

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Re: Fields Medals 2026

#61

Post by Onavo »

frakt0x90 wrote: post #33
siva7 wrote: post #20

"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…

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.

> Lysing action of the (1,2)b-carotene receptive encephalopathy pathway

High school biology is enough to get a vague idea of this though.

Re: Fields Medals 2026

#62

Post by nl »

vonneumannstan wrote: post #15
unethical_ban wrote: post #5

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.

[flagged]

Tsimerman's work is directly applicable in two fields of computer science: O-minimality can be used to simplify formal verification.

Re: Fields Medals 2026

#63

Post by CamperBob2 »

vonneumannstan wrote: post #15
unethical_ban wrote: post #5

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.

[flagged]

Username sure as hell does not check out

Re: Fields Medals 2026

#64

Post by CamperBob2 »

applfanboysbgon wrote: post #55
falcor84 wrote: post #41

Earlier quoted context omitted.

> 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.

The only thing I can think is ... how? If I were to anthromorphize my experience with frontier models, it would be as a mentally challenged child with complete memorization of an encyclopedia and thesaurus. It has the ability to rapidly experiment and potentially succeed at tasks through trial-and-error, but not without constantly corralling it in the correct direction because it would stick a fork in an outlet if un…

If I were to anthromorphize my experience with frontier models, it would be as a mentally challenged child with complete memorization of an encyclopedia and thesaurus.

Memorizing an encyclopedia is not going to help you solve open high-level math problems, is it?

Re: Fields Medals 2026

#65

Post by nl »

leonvoss wrote: post #49
orochimaaru wrote: post #44

Earlier quoted context omitted.

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…

Quantitative scientists are also mathematicians. I'm not attacking mathematics, just probably-useless subfields. Is there any good quantitative evidence that actually estimates what percent of math work today will be useful? Because to me it seems like <1% and I feel like we could easily make that number a lot higher. Particularly I want to see massive improvements in quantitative social science; physics already gets…

Here are a couple of Fields medalists' work that had direct practical applications less than 5 years after publication:

Terence Tao's work (with Emmanuel Candès and Justin Romberg) on compressed sensing. Published in 2004-05. By 2007 that was being used for in-vivo MRI reconstruction with substantially undersampled data

June Huh's work on combinatorial Hodge theory was used within 3 years to improve sampling for random spanning forests.

Note that this is only Fields medalists (not all pure mathematics). There have been huge improvements in zero knowledge proofs and homomorphic encryption over the last ~5 years that are also directly applicable to pure mathematics, but no one has a Fields medal for it.

Re: Fields Medals 2026

#66

Post by nl »

neaden wrote: post #18
netvarun wrote: post #12

Earlier quoted context omitted.

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…

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.

It's wrong - most of this work was published before 2024.

But Tsimerman in particular is very AI pilled and has talked about how he thinks LLMs will be doing better work that most mathematicians in 2 years: https://x.com/gbrl_dick/status/2080416238606717052

(He's just been hired by OpenAI)

Re: Fields Medals 2026

#67

Post by cindyllm »

applfanboysbgon wrote: post #55
falcor84 wrote: post #41

Earlier quoted context omitted.

> 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.

The only thing I can think is ... how? If I were to anthromorphize my experience with frontier models, it would be as a mentally challenged child with complete memorization of an encyclopedia and thesaurus. It has the ability to rapidly experiment and potentially succeed at tasks through trial-and-error, but not without constantly corralling it in the correct direction because it would stick a fork in an outlet if un…

[dead]

Re: Fields Medals 2026

#68

Post by azan_ »

fn-mote wrote: post #39
azan_ wrote: post #28

Earlier quoted context omitted.

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.

It's not, it's basically something that happened. One unsolved problem was solved with the only human input being telling LLM to work harder and to actually solve it after few failed attempts.

Re: Fields Medals 2026

#69

Post by nerdsniper »

Onavo wrote: post #61
frakt0x90 wrote: post #33

Earlier quoted context omitted.

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.

> Lysing action of the (1,2)b-carotene receptive encephalopathy pathway High school biology is enough to get a vague idea of this though.

Right. With a college degree, I understand most of these words. I don’t have a clue about the impact of the research or how it fits into the corpus, but I understand the gist of the article title.

Despite my degree being in engineering, which involved 4 semesters of calculus, and 3 other semesters of math, (7 total) I have absolutely no fucking clue what’s going on in the Fields Medal description above. It’s only barely more intelligible than if it had been written in Chinese (which I truly cannot read at all).

I genuinely don’t understand it at all. Even words that I think I recognize like “harmonic” or “geometric” are useless to me because the actual terms are “harmonic analysis” and “geometric measure theory” and I have 0% clue what those are.

I don’t have to google any of the words in the example biology title.

Re: Fields Medals 2026

#70

Post by CamperBob2 »

feyman_r wrote: post #48
siva7 wrote: post #20

"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…

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.
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