Fields Medals 2026 • Hacker News Board

Re: Fields Medals 2026

#41

Post by falcor84 » Thu, Jul 23, 2026, 9:25 PM UTC

applfanboysbgon wrote: post #23

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

"Looks like" being the operative keyword there. 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. The whole point is that, even though these things are really good at generating what looks like human output, they are still just regular software algorithms.

> 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.

Re: Fields Medals 2026

#42

Post by pmontra » Thu, Jul 23, 2026, 9:26 PM UTC

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.

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.

Re: Fields Medals 2026

#43

Post by blovescoffee » Thu, Jul 23, 2026, 9:26 PM UTC

BeetleB wrote: post #25

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.

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?

Re: Fields Medals 2026

#44

Post by orochimaaru » Thu, Jul 23, 2026, 9:30 PM UTC

leonvoss wrote: post #31

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.

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.

Re: Fields Medals 2026

#45

Post by netvarun » Thu, Jul 23, 2026, 9:39 PM UTC

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.

https://x.com/Qiaoqiao2001/status/2080003441821163958

While there was a bunch of human effort - it is not that hard to imagine this whole pipeline becoming fully autonomous in the coming months.

Re: Fields Medals 2026

#46

Post by energy123 » Thu, Jul 23, 2026, 9:41 PM UTC

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, non-human corpus) that has no obvious upper bound on capabilities.

Re: Fields Medals 2026

#47

Post by BeetleB » Thu, Jul 23, 2026, 9:52 PM UTC

blovescoffee wrote: post #43

BeetleB wrote: post #25

Earlier quoted context omitted.

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?

Yes - as in you have thousands, if not tens of thousands of folks around the world who can understand the general ideas of what was worked on.

Re: Fields Medals 2026

#48

Post by feyman_r » Thu, Jul 23, 2026, 10:07 PM UTC

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...

Re: Fields Medals 2026

#49

Post by leonvoss » Thu, Jul 23, 2026, 10:14 PM UTC

orochimaaru wrote: post #44

leonvoss wrote: post #31

Earlier quoted context omitted.

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…

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 a lot of attention so it wouldn't be able to see as much improvement to getting more resources but it could probably still get more.

Re: Fields Medals 2026

#50

Post by solomonb » Thu, Jul 23, 2026, 10:25 PM UTC

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.