ai in mathematics

@QuanquanGu

2026-09-12 — saved image

Quanquan Gu @QuanquanGu · 2h
Just got this incredible news from UCLA Math Circle.

Two high school students, Aayush Bathija and Prince Rohatgi, working with postdoc Daniel Soskin through the UCLA Math Circle, have solved a problem that Fields Medalist June Huh had previously worked on without solving.

The paper was heavily AI-assisted.

Whatever your view on AI in mathematics, enabling high school students to push the frontier of mathematical research is something worth celebrating.

[link card]
arxiv.org
Bounded ratios for Lorentzian polynomials

ai in mathematicslorentzian polynomialsjune huharxivai-assisted researchhigh school students

Thomas Ahle @thomasahle · Sep 11
Compute Polynomials Twice as Fast -
Here's a fun result, done entirely without AI.

That because we proved it years ago, but it ran a hundred pages and we weren't quite sure enough to publish. Now AI verified it in Lean.

A fun fact about polynomials is that
P(x) = x⁴ + a₃x³ + a₂x² + a₁x + a₀
can be evaluated in just two(!) multiplications!

The trick is to write
y = (x + b₀)x + b₁
P(x) = (y + x + b₂)y + b₃
where b₀...b₃ are easy to calculate from a₀...a₃.

Polynomials are everywhere from computing exp/sin, to cryptographic hashes and codes. Over finite fields multiplications are particularly expensive, so a 2x speedup matters.

Donald Knuth and others showed ~n/2 multiplications suffice for any degree n, but their preprocessing needs complex roots: numerically unstable and useless over finite fields. Rabin & Winograd fixed that with rational preprocessing, but 2logn extra multiplications, which hurts at the small n we most care about.

Our new method solves this. It uses ⌈(n+1)/2⌉ multiplications, and we prove this is optimal.

You can try it out on your own polynomials at
thomashale.com/fast-polynomia… [cut off]

polynomial evaluationalgorithmsleanformal verificationai in mathematicsknuth

@blingdivinity

2026-09-12 — saved image

bling @blingdivinity · 17h
root complaint sounds like: truth and understanding used to be bundled as one job. now ai finds the truth and and humans are left producing understanding. but nobody funds understanding without the prestige of new truths. so we get undigestible slop proofs that dont advance broader mathematics or science.

so theres a tractable fix: reweight prestige towards understanding-generation.

[quoted post]
Andrew Curran @AndrewCurran_ · 19h
Twenty-five Fields Medal winners have published a joint declaration warning about what they see as a severe misalignment between AI companies and the mathematics community.

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A Severe Misalignment of AI in Mathematics

Over the last few months, the mathematical capabilities of LLMs have improved dramatically, to the point that they can solve major outstanding problems in many fields of mathematics. However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned. We see these as part of broader alignment issues impacting other scientific and creative professions, as well as the whole of society.

ai in mathematicsfields medalmisalignmentbenchmarksmath communityunderstanding vs truth