Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Fields Medals 2026

mathunion.org

Post reply on HN
Print view View original

81–90 of 128 posts

Re: Fields Medals 2026

#81

Post by j16sdiz »

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 think most undergrad level course on probability expose you to measure theory _without_ telling you they are measure theory.

Re: Fields Medals 2026

#83

Post by bananaflag »

Ar-Curunir wrote: post #73
MattCruikshank wrote: post #26

Earlier quoted context omitted.

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.

Because in chess you can be sure that no AI was used (and even there, there are controversies, see the recent Niemann/Carlsen scandal). Since math is not usually done in public, under competition rules, no one will know ever again whether some result was really obtained by a human.

Re: Fields Medals 2026

#84

Post by bananaflag »

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…

Read these 4 prompts and tell me again how in the future we shall still need human expertise:

https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...

Re: Fields Medals 2026

#85

Post by ares623 »

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

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.

Re: Fields Medals 2026

#86

Post by mmooss »

goodmythical wrote: post #77
fn-mote wrote: post #40

Earlier quoted context omitted.

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

That links to The 17-Year-Old Student Who Solved a Major Math Mystery, about Hannah Cairo.

Re: Fields Medals 2026

#87

Post by raverbashing »

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…

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.

Re: Fields Medals 2026

#88

Post by yablak »

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.

if you took an engineering course that covered fourier transform, z transform, or laplace transform, then you have seen an introduction to harmonic analysis on the circle and the real number line.

typically when I see mentions of harmonic analysis together with differential geometry I start thinking of fourier transform on more fancy shapes (on the sphere, for example, the replacements for complex exponentials are called spherical harmonics)

my PhD was EE in signal processing and I took some extra math classes at the graduate level, and continue to read some of this for fun and profit.

I still cant understand most of the terminology in the fields medal citations. that probably requires a more thorough couple of years of graduate education in mathematics.

math is by far the furthest of the sciences in terms of depth of human discovery.

Re: Fields Medals 2026

#89

Post by walrus01 »

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

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.

Re: Fields Medals 2026

#90

Post by Jach »

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.

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.
Post reply on HN