Tom Gur

Tom Gur

@tomgur.bsky.social

Professor of Computer Science at Cambridge.

1K followers177 following85 posts

Tom Gur reposted

An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4

Tom Gur reposted

Tom Gur reposted

Many people with relevant expertise think there's a real chance that AI could kill us all in the not too distant future. Others disagree. I've written a post, aimed principally at mathematicians, detailing my struggles to decide what to make of this. gowers.wordpress.com/2026/10/16/h...

gowers.wordpress.comHow worried should we be about extinction risk from AI?A little over two months ago, Jacob Tsimerman surprised a lot of people by announcing, immediately after he had received a Fields Medal, that he would be giving up mathematical research and “…

Tom Gur reposted

We're excited that our researchers @tomgur.bsky.social @martin.kleppmann.com & Amanda Prorok are receiving funding from the @aria-research.bsky.social 'Scaling Trust' programme to lead teams exploring ambitious new ways of improving #AI security. Read about their projects here: shorturl.at/8K1ck

With the capability to coordinate securely, AI agents could act reliably on our behalf, unlocking a whole range of interactions that were previously inaccessible. Meet the first teams we’re backing to build the open-source tools to make it happen: https://link.aria.org.uk/ST-Creators

Tom Gur reposted

Tom Gur reposted

Tom Gur reposted

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-...

openai.comAn OpenAI model has disproved a central conjecture in discrete geometryAn 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.

Tom Gur reposted

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

Postdoc position in Cambridge with the amazing Anuj Dawar!

There is a post-doctoral position available in my group. Funding is for two years in the first instance (with a possibility of an extension). Details on how to apply are at the link below. Please feel free to contact me with any enquiries. www.cam.ac.uk/jobs/researc...

Tom Gur reposted

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.

gowers.wordpress.comGroup and semigroup puzzles and a possible Polymath projectAn 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…

Happy days! A perfect excuse to share my favourite quantum cryptography origin story, as recounted in Brassard’s paper: arxiv.org/pdf/quant-ph...

Congratulations to Charles H. Bennett and Gilles Brassard on receiving the 2025 ACM A.M. Turing Award! They are recognized for their essential role in establishing the foundations of quantum information science and transforming secure communication and computing. awards.acm.org/turing @umontreal

A quantum computer here at Cambridge!

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

arxiv.orgThe Lens of Abelian EmbeddingsWe 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...

Tom Gur reposted

Theoretical CS community! I have a small favor to ask. If you ever used, read, watched some of the (excellent IMO) exposition content by Ryan O'Donnell, would you mind filling this very short survey, and maybe say how useful to you it was? 📝 forms.gle/xrvc2mLRbMqK... Please spread this! #TCSSky

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...

Tom Gur reposted

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.netmichel.talagrand.net
arXiv math.PR Probability@mathpr-bot.bsky.social

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

Tom Gur reposted

Reminder: the School of Computer Science at #USyd is hiring across the board, equiv. tenure-track positions! Join us at @sydney.edu.au! Deadline ⏰ December 1 🇦🇺

The School of #ComputerScience at #USyd is hiring! Multiple continuing (≡ tenure-track) positions in all areas, with particular focus on the ones listed below. Women and candidates from underrepresented groups are encouraged to apply. ⏰ Apply by Dec 1: usyd.wd105.myworkdayjobs.com/en-GB/USYD_E...

I’m looking for postdocs and PhD students to join my group at Cambridge! Topics include: Classical & Quantum Complexity, Sublinear Algorithms, Coding Theory, Cryptography, Learning Theory, and their interplay with Fourier Analysis & Additive Combinatorics. To apply or inquire, email me your CV.