Monthly Archives: September 2025

Dror Bar-Natan and Roland Van der Veen – A Fast, Strong, and Fun knot invariant!

Posted on September 25, 2025 by Gil Kalai

Dror Bar-Natan (homepage, Wikipedia) told me about his work with Roland Van der Veen (homepage, arXiv, YouTube) on a wonderful knot invariant which distinguishes knots much better than other knot invariants, and can be computed quickly even for knots of … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Geometry | Tagged , , | 1 Comment

Polynomial Bounds for Chowla’s Cosine Problem

Posted on September 17, 2025 by Gil Kalai

Polynomial bounds for the Chowla cosine problem were achieved independently in two very recent works. Zhihan Jin, Aleksa Milojević, István Tomon, Shengtong Zhang: From small eigenvalues to large cuts, and Chowla’s cosine problem; Benjamin Bedert: Polynomial bounds for the Chowla Cosine Problem Abstract … Continue reading →

Posted in Analysis, Combinatorics | Tagged , , , , , | 2 Comments

Maria-Romina Ivan and Sean Jaffe: The saturation number for the diamond is linear

Posted on September 13, 2025 by Gil Kalai

My previous post was about an asymptotic solution of Rota’s basis conjecture and the next few posts will also be devoted to some mathematical news. Before moving to the main featured result let me mention a beautiful blog post by … Continue reading →

Posted in Combinatorics | Tagged , , | 1 Comment

Richard Montgomery and Lisa Sauermann Present Major Progress on Rota’s Basis Conjecture

Posted on September 9, 2025 by Gil Kalai

Richard Montgomery and Lisa Sauermann: Asymptotically-tight packing and covering with transversal bases in Rota’s basis conjecture Abstract: In 1989, Rota conjectured that, given any bases of a vector space of dimension , or more generally a matroid of rank , … Continue reading →

Posted in Combinatorics, Open problems | Tagged , , , | 2 Comments

ChatGPT is a Useful but Demanding Mathematical Collaborator

Posted on September 5, 2025 by Gil Kalai

ChatGPT was very useful in explaining (and discussing) some mathematical issue with me. Here is how our conversation had concluded. (In case ChatGPT reads this post, let me emphasize: this is a praise and not a complaint.) Me:  Thank you … Continue reading →

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