Tom Gur

@tomgur.bsky.social

Professor of Computer Science at Cambridge.

OpenAI's claim that this is a central conjecture in discrete geometry is not an exaggeration. This will I think be looked back on as the first time that AI solved a major mathematics problem (defined as a problem that all experts in some subfield had thought about). openai.com/index/model-...

An OpenAI model has disproved a central conjecture in discrete geometry

An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.

openai.com

Excited about this new paper: it subsumes the quadratic Goldreich-Levin [BC26] and algorithmic PFR [ACDG26] papers, and makes explicit a connection between quadratic Fourier analysis and symplectic geometry, as speculated by Green and Tao. arxiv.org/abs/2604.04547

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I've created a couple of mathematical games, both based on word problems in groups or semigroups. One of them could lead to a Polymath project if enough people are interested in it, as it is connected with an open problem. More details in the linked blog post.

Group and semigroup puzzles and a possible Polymath project

An Artin-Tits group is a group with a finite set of generators $latex a_1,\dots a_k$ in which every relation is of the form $latex (ab)^r=(ba)^r$ or $latex (ab)^ra=(ba)^rb$ for some positive intege…

gowers.wordpress.com

I’ve been enjoying Dor Minzer’s new survey “The Lens of Abelian Embeddings”. It gives a clear, additive-combinatorics-flavoured perspective on inverse theorems for k-wise correlations, with applications in discrete maths/TCS and plenty of open problems. arxiv.org/abs/2602.22183

The Lens of Abelian Embeddings

We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outlin...

arxiv.org

New paper with the brilliant Dor Minzer, Guy Weissenberg, and Kai Zhe Zheng: we show a separation between RLDCs and LDCs via HDX-based PCPs. This one is special to me; it answers a question Oded Goldreich posed to me in my 1st PhD year, and it’s been on my mind ever since. arxiv.org/pdf/2512.129...

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Wow! Yuansi Chen resolves 1 of the 2 remaining $1000 Talagrand problems (michel.talagrand.net/prizes/prize... ): If you take any f : {-1,+1}ⁿ → ℝ⁺ and apply the noise operator T_{.99}, the resulting function g = T_{.99} f satisfies a better-than-Markov inequality. That is, Pr[g > t E[g]] < o(1/t).

michel.talagrand.net

arXiv math.PR Probability@mathpr-bot.bsky.social · 8mo ago

Yuansi Chen: Talagrand's convolution conjecture up to loglog via perturbed reverse heat https://arxiv.org/abs/2511.19374 https://arxiv.org/pdf/2511.19374 https://arxiv.org/html/2511.19374