I’ve just uploaded to the arXiv my paper “On product representations of squares“. This short paper answers (in the negative) a (somewhat obscure) question of Erdös. Namely, for any , let b...
https://terrytao.wordpress.com/2024/05/20/on-product-representations-of-squares/
The purpose of this post is to report an erratum to the 2012 paper “An inverse theorem for the Gowers -norm” of Ben Green, myself, and Tamar Ziegler (previously discussed in this blog post). ...
https://terrytao.wordpress.com/2024/04/25/erratum-for-an-inverse-theorem-for-the-gowers-us1n-norm/
A recent paper of Kra, Moreira, Richter, and Robertson established the following theorem, resolving a question of Erdös. Given a discrete amenable group , and a subset of , we define the Banach ...
https://terrytao.wordpress.com/2024/04/24/notes-on-the-bbt-theorem/
This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assist...
Tim Gowers, Ben Green, Freddie Manners, and I have just uploaded to the arXiv our paper “Marton’s conjecture in abelian groups with bounded torsion“. This paper fully resolves a conjecture ...
https://terrytao.wordpress.com/2024/04/04/martons-conjecture-in-abelian-groups-with-bounded-torsion/
The first progress prize competition for the AI Mathematical Olympiad has now launched. (Disclosure: I am on the advisory committee for the prize.) This is a competition in which contestants subm...
Earlier this year, I gave a series of lectures at the Joint Mathematics Meetings at San Francisco. I am uploading here the slides for these talks: I also have written a text version of the first ...
Let be a non-empty finite set. If is a random variable taking values in , the Shannon entropy of is defined as There is a nice variational formula that lets one compute logs of sums of exponentia...
In my previous post, I walked through the task of formally deducing one lemma from another in Lean 4. The deduction was deliberately chosen to be short and only showcased a small number of Lean t...
https://terrytao.wordpress.com/2023/12/05/a-slightly-longer-lean-4-proof-tour/
Since the release of my preprint with Tim, Ben, and Freddie proving the Polynomial Freiman-Ruzsa (PFR) conjecture over , I (together with Yael Dillies and Bhavik Mehta) have started a collaborati...