My host at Brown University was the fascinating Basilis Gidas whom I first met in Rio in 2018. Basilis has had a remarkable career, taking him from electrical and mechanical engineering through qua…

What is mathematics? Over the years I devoted a few dozen posts to the question “What is mathematics?”.  Some posts in this category bring tears to my eyes like Christine Bjorner’…

The θ(p꜀) = 0 conjecture is solved in all dimensions. In 2024 Gady Kozma and Shahaf Nitzan showed how to derive the dying percolation conjecture from a proposed conjecture about percolation on gene…

Yuval Boger interviews mathematician Gil Kalai about his long-standing skepticism regarding scalable quantum computing. Kalai explains two main arguments behind his theory: correlated noise that may d...

ICM2026 in Philadelphia was, for me, a celebration of mathematics and people. I met many friends and colleagues, as well as several mathematical ideas and results. The nature of these meetings is t…

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…

In this post present 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…

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…

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. Do…

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…

Happy Chanukah, everybody! There is a lot of academic activity around, and the ceasefire in Gaza has brought some relief and hope. Let me tell you about the (unusually high number of) lectures I at…

Two weeks ago I was invited together with my colleague Shay Mozes to visit the Israeli Quantum Computing Center located near the Tel Aviv University quite close to my home. That morning my wife tol…

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…

The purpose of this question is to collect examples where large language models (LLMs) like ChatGPT have led to notable mathematical developments. The emphasis in this question is on LLMs, but ans...

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…

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 …

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 …

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…

Let me briefly report on two birthday conferences for long-time friends and colleagues Saharon Shelah and Yuri Gurevich. Yuri fest took place in Munich and on Zoom between June 20–22 2025 and Shela…

Three pictures showing that the media control symbol “play” was successfully embedded into London’s skyline. The fourth rare picture is a screenshot with the control symbol &#8220…

A brief update: Since Friday June 13 Israel has been engaged in a direct war with Iran. This follows two major missiles attacks of Iran against Israel in April and October 2024, as well as Iran’s c…

Recommend watch before the talk: https://www.youtube.com/live/ykBkZB8JiCg?si=YFijp9gUCdF82je_ Abstract from Gil Kalai: Quantum computers are fascinating hypothetical powerful computers and the debate...

As part of a day-long meeting on organization of science in Prague, I gave a 10-minite presentation on Science and Diversity in a small Country (click for my slides) and devoted a few minutes and o…

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…

As many of you likely heard by now, Hong Wang and Joshua Zahl proved the Kakeya’s Conjecture in three dimensions. Hong Wang and Joshua Zahl, Volume estimates for unions of convex sets, and th…

In a previous post I presented the skeptical views toward quantum computing of Robert Alicki, Michel Dyakonov, Leonid Levin, Oded Goldreich, Liam McGuinness, Moshe Vardi and a few others. As I ment…

This post contains the first item, devoted to Majorana zero modes, from an ambitious planned post on some quantum physics mysteries, related to quantum information and computation. (Some items are …

In this post, I provide links, references, and a brief discussion of the skeptical views regarding quantum computing held by Robert Alicki, Michel Dyakonov, Leonid Levin, Oded Goldreich, and a few …

Here is a roadmap for the debate about quantum computers from my perspective. Skeptical claims are in blue, responses to these claims are in purple. Points 1-8 represent skeptical claims made over …

The purpose of this post is to present seven assertions about quantum computing that arose in my research. I welcome questions and remarks and will gladly clarify or elaborate on them.