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Gil Kalai @GilKalai
Joined March 2013
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@SebastienBubeck
May 20
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An internal model of Open AI disproved Erdos unit distance conjecture. gilkalai.wordpress.com/2026/…

Amazing: Erdős’ Unit Distance Problem was Disproved! It was achieved by AI!

Paul Erdős’s, in his 1946  paper published in the American Mathematical Monthly, posed two general questions about the distribution of distances determined by a finite set of points in a metr…

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We launched this preliminary polymath AI project. Participation is welcome! gilkalai.wordpress.com/ai/op…

Optimal Monotone Families for the Discrete Isoperimetric Inequality

A Polymath Project with AI Agents April 5, 2026 In this post we launch what may be among the first Polymath-style mathematical projects involving both human participants and AI agents. This directi…

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Nissan Hajaj proposes to merge polymath projects with AI. gilkalai.wordpress.com/2026/…

Polymath Plus AI

This post was written together with Nissan Hajaj and Ido Kaminer.  Update (April 5, 2026): The first project is launched here. AI and Math has become a hot topic (and a source of some worries) amon…

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Kazhdan seminar on Boolean Functions, Hypercontractivity, and Applications has started today (on Zoom). We will run the seminar also next week, March 29. gilkalai.wordpress.com/2026/…

Starting Today: Kazhdan Sunday seminar: “Boolean Functions, Hypercontractivity, and Applications”

Sunday, 22 March, 2026 – 11:00 to 13:00 Today the seminar will take place via zoom. After Pesach we hope to make it in Ross 70 seminar room.   Repeats every week every Sunday until the end of…

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In an interview with Yuval Boger, Scott Aaronson thoughtfully presents his view of my position about quantum computers. My post contains a few responses. gilkalai.wordpress.com/2026/…

Scott Aaronson’s View of my View About Quantum Computing

This post presents a very good interview of Scott Aaronson with Yuval Boger of QuEra, in which Scott gives a detailed and thoughtful account of his view of my position. Scott nicely characterizes t…

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Twenty years ago, I raised the Fully Depolarizing Noise Conjecture for Physical Bell States, which, if holds, be a major obstruction for quantum computation. gilkalai.wordpress.com/2026/…

The Fully Depolarizing Noise Conjecture for Physical Cat States is Twenty Years Old!

Amidst the war, I am holding onto hope for a future of peace and tolerance. At the end of the post I include a few pictures from the safe room (closet). Writing this also made me reflect on related…

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Updates, plans, very many mathematical problems, and congratulations to Benjy Weiss - the Israel Prize recipient for 2006. gilkalai.wordpress.com/2026/…

Updates and Plans V: From Boise to Tel Aviv, Ceasefire, My 70th Birthday, Nostalgia, Problems,...

This is the fifth post of this type (I (2008); II(2011); III(2015); IV(2024)). Between Boise and Tel Aviv During the summer we spent two months in the lovely city of Boise, Idaho. We stayed with my…

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Has quantum advantage been achieved? gilkalai.wordpress.com/2026/…

Dominik Hangleiter’s View Posts on: Has Quantum Advantage Been Achieved?

In a recent post on Quantum Frontiers—the first in a series of three—Dominik Hangleiter discusses the question of whether quantum advantage (also known as “quantum supremacy”) has been achieved. (U…

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Can you identify the mathematicians in the picture? gilkalai.wordpress.com/2026/…

A Ten-Year-Old Video about Larry Guth and Netz Katz.

Facebook recently reminded of a videotaped lecture I gave ten years ago on Larry Guth and Nets Katz. In that lecture, I discussed their famous joint work on the Erdős distinct distances problem, as…

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A very nice short video by Sabine Hossenfelder about quantum computing scepticism. youtu.be/WeVGJr6h-CQ?si=rkeb…
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Some combinatorics news gilkalai.wordpress.com/2026/…

Combinatorics News

Happy new 2026 to all our readers! Here are some very interesting combinatorics results that I learned about recently. I will try to write in some more details about some of them later on.  1) Gaus…

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Gil Kalai@GilKalai
3 Nov 2025
The role of computational complexity to restrict physical theories. My perspective on a recent lecture by Scott Aaronson. gilkalai.wordpress.com/2025/…

Computational Complexity and Explanations in Physics

The title of this post is taken from a recent interesting lecture (judging from the slides) by Scott Aaronson at Columbia University. The lecture explored a wide range of topics at the intersection…

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Gil Kalai@GilKalai
28 Oct 2025
I asked in Math Overflow about Mathematical developments assisted (or achieved) using LLMs (like ChatGPT). mathoverflow.net/questions/5…

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Gil Kalai@GilKalai
29 Sep 2025
The remarkable progress by Bo'az Klartag on the sphere packing problem in high dimensions, and the question: what is the answer? Is it close to Bo'az new lower bound, or perhaps exponentially better? gilkalai.wordpress.com/2025/…

Bo’az Klartag: Striking new Lower Bounds for Sphere Packing in High Dimensions

Two day ago, a new striking paper appeared on the arXiv Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid, by Bo’az Klartag. Abstract: We prove that in a…

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Gil Kalai@GilKalai
25 Sep 2025
A wonderful breakthrough by Dror Bar-Natan and Roland Van der Veen. Knot invariants which can be computed for diagrams with hundreds of crossings, are powerful, and carry profound dreams and conjectures. gilkalai.wordpress.com/2025/…

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

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 i…

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Gil Kalai@GilKalai
12 Sep 2025
Asymptotic version of the Rota Basis Conjecture was proved! gilkalai.wordpress.com/2025/…

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

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 $latex n…

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Gil Kalai@GilKalai
30 Jul 2025
gilkalai.wordpress.com/2025/… Recently, I have given several lectures about quantum computation, presenting my argument for why quantum computing—and even significant early milestones toward it—are fundamentally impossible. The post list 48 interesting questions from these events.

Some Questions from Recent Quantum Events

Over the past few years, I have given several lectures about quantum computation, presenting my argument for why quantum computing—and even significant early milestones toward it—are fundamentally …

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Gil Kalai@GilKalai
23 Jul 2025
After 78 years, an exponential improvement for Ramsey numbers were found by Jie Ma, Wujie Shen, and Shengjie Xie. gilkalai.wordpress.com/2025/…

Amazing: Jie Ma, Wujie Shen, and Shengjie Xie Gave an Exponential Improvement for Ramsey Lower Bo...

h/t Benny Sudakov The Ramsey number R(ℓ,k) is the smallest integer n such that in any two-coloring of the edges of the complete graph on n vertices, $latex K_n$, by red and blue, there is either a …

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Gil Kalai@GilKalai
15 Jul 2025
My summary of Joram's seminar on Hypercontractivity and groups. Speakers: Noam Lifshitz, Dor Minzer, Nathan Keller and Guy Kindler. gilkalai.wordpress.com/2025/…

Joram’s seminar 2025: Hypercontractivity, Groups and Representations

Joram’s seminar 2025 Here is my summary of the recent Joram’s seminar that took place on July 9 and 10 in Jerusalem. Much of the seminar was about the the paper Product Mixing in Compac…

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