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Fields Medals 2026

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Re: Fields Medals 2026

#71

Post by Ar-Curunir »

nerdsniper wrote: post #69
Onavo wrote: post #61

Earlier quoted context omitted.

> 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 bar…

Did your 7 semesters of calculus include any courses that a math major would take?

For example, a single upper-division undergrad level course on probability will expose you to measure theory.

Similarly, harmonic analysis is something that you can take as a reasonably good senior in mathematics.

Re: Fields Medals 2026

#72

Post by falcor84 »

anvuong wrote: post #59
falcor84 wrote: post #19

Earlier quoted context omitted.

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

Well, how many humans do you think are able to prompt this to the LLM? "The homogeneity in x is an intertwining between a dilation (x,r,u) to (lambda x, r,u) and a dilation (P,Q,R) to (lambda^-2 P, lambda^-1 Q, lambda R) which seems to collapse the 3d jacobian to a sort of twisted 2d jacobian. Is there a general theory of such twisted jacobians and do you have any sense why those particular dilation weights were used…

I don't get the argument. It sounds to me like you're saying that because my own chess skills are insufficient to allow me to have a proper game with a grandmaster and I end up losing on move 10 because after a stupid blunder, then I should conclude that this grandmaster is just a tool?

Re: Fields Medals 2026

#73

Post by Ar-Curunir »

MattCruikshank wrote: post #26
Laurel1234 wrote: post #4

Earlier quoted context omitted.

[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.

We don't call those bots grandmasters and have them compete in championships, nor do we laud them for beating human grandmasters.

Re: Fields Medals 2026

#74

Post by WarmWash »

energy123 wrote: post #46
hackandthink wrote: post #34

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, no…

The obvious and primary application will not be on showy millennium problems or long sought conjectures, but on optimizations and breakthroughs surrounding transformers.

Re: Fields Medals 2026

#75

Post by nerdsniper »

Ar-Curunir wrote: post #71
nerdsniper wrote: post #69

Earlier quoted context omitted.

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 bar…

Did your 7 semesters of calculus include any courses that a math major would take? For example, a single upper-division undergrad level course on probability will expose you to measure theory. Similarly, harmonic analysis is something that you can take as a reasonably good senior in mathematics.

I took multivariate calculus (I to III), differential equations, statistics, discrete math, and linear algebra.

I didn't take those courses you're talking about, but that's my point. I have a top <1% education in math in the nation, maybe top 2-3% of all college grads, and that's not enough to even scratch the surface of the summary.

Re: Fields Medals 2026

#76

Post by Onavo »

nerdsniper wrote: post #75
Ar-Curunir wrote: post #71

Earlier quoted context omitted.

Did your 7 semesters of calculus include any courses that a math major would take? For example, a single upper-division undergrad level course on probability will expose you to measure theory. Similarly, harmonic analysis is something that you can take as a reasonably good senior in mathematics.

I took multivariate calculus (I to III), differential equations, statistics, discrete math, and linear algebra. I didn't take those courses you're talking about, but that's my point. I have a top <1% education in math in the nation, maybe top 2-3% of all college grads, and that's not enough to even scratch the surface of the summary.

Well, the snobby pure maths folks look down on applied engineering math ;)

Re: Fields Medals 2026

#77

Post by goodmythical »

fn-mote wrote: post #40
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…

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

Re: Fields Medals 2026

#78

Post by num42 »

netvarun wrote: post #12
num42 wrote: post #3

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…

"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.

Re: Fields Medals 2026

#79

Post by applfanboysbgon »

CamperBob2 wrote: post #64
applfanboysbgon wrote: post #55

Earlier quoted context omitted.

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?

> 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

It kind of could, given the above. Part of an LLM's advantage is that, much like a calculator or a Chess engine, it can iterate over a finite problem space far, far faster than a human can. That much is expected of a useful computing tool.

It is worth noting that we know literally nothing about how the counterexample was achieved. Technically speaking, the person who tweeted it could have solved it themselves with zero LLM assistance and then attributed it to Fable to boost their IPO and ensuing payday. I'm not saying that's actually what happened, but it's hard to draw conclusions without any transparency about the degree of human involvement.

My daily experience certainly does not reflect that of prompting a superhuman intelligence when it routinely flubs commands and destructively drops the PATH of its vm, or bypasses an instruction about passing tests by burning millions of tokens constructing a completely new test suite that rubberstamps its own work when it can't pass the real tests.

Re: Fields Medals 2026

#80

Post by _carbyau_ »

solomonb wrote: post #50
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…

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?"

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