Examples for the use of AI and especially LLMs in notable mathematical developments 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...

mathoverflow.net/questions/50...

I posted a question on Math Overflow on the use of LLMs (such as ChatGPT) in mathematics.

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…

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, fun, and carry profound dreams and conjectures.
gilkalai.wordpress.com/2025/09/25/d...

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 …

48 interesting questions from the audience of recent lectures about quantum computation, where I presented my argument for why quantum computing—and even significant early milestones toward it—are fundamentally impossible.

gilkalai.wordpress.com/2025/07/30/s...

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

After 78 years, an exponential improvement for Ramsey numbers were found by Jie Ma, Wujie Shen, and Shengjie Xie.
gilkalai.wordpress.com/2025/07/23/a...

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…

Joram’s seminar 2025: Hypercontractivity, Groups and Representations. Splendid connections between combinatorics, algebra, analysis, and geometry, using representation theory and hypercontractivity. There are some applications to TCS and physics.

gilkalai.wordpress.com/2025/07/15/j...

Happy Birthday Saharon Shelah and Yuri Gurevich! 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…

Birthday conferences for Saharon Shelah and Yuri Gurevich, and a lecture by Ronald de Wolf on quantum proofs for classical theorems.

gilkalai.wordpress.com/2025/07/07/h...

A Breakthrough of an Unusual Nature: the Media Control Symbol “Play” was Successfully Embedded into the London Skyline! 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 Remarkable discovery in London's skyline!

gilkalai.wordpress.com/2025/06/27/a...

Shakhar Smorodinsky’s Solution to a Radon-Type Problem 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…

Shakhar Smorodinsky settled (on the spot) an old Radon-type problem that I posed in the 70s. In addition, an update, pictures from the recent Erdos lecture by Mehtaab S. Sawhney, and some light on the mysterious huge digital thermometer in our lecture hall. gilkalai.wordpress.com/2025/06/18/s...

[Invited talk] Gil Kalai: A critical view on quantum computing 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...

Later today, (17:00 Israel time, June 3) I give a zoom lecture followed by conversation: A critical view on quantum computing, at the Ethereum foundation. There will also be a live streaming, open to all, here: youtube.com/live/HhWWkTk...

Logic at HUJI 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…

One slide on the amazing story of mathematical logic at the Hebrew University of Jerusalem.
gilkalai.wordpress.com/2025/05/28/l...

Very nice thread. Thanks for listening and reporting!

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…

Sphere packing problem - amazing progress by Bo'az Klartag
gilkalai.wordpress.com/2025/04/09/b...

Hong Wang and Joshua Zahl’s Solution for Kakeya’s Problem in Three Dimensions – Reflections and Links 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…

Hong Wang and Joshua Zahl’s Breakthrough on Kakeya’s Problem in Three Dimensions: Insights and Resource
gilkalai.wordpress.com/2025/04/04/h...

Survivorship bias - Wikipedia

I recognized the right picture from en.wikipedia.org/wiki/Survivo... ; What is the point?

Quantum Computing Skepticism, Part 2: My View and Responses to Skeptical Claims—Featuring John Preskill, Scott Aaronson, Dave Bacon, Aram Harrow, and Boaz Barak 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…

The second part of my post on quantum computer skepticism featuring my own view and some counter arguments to various skeptical claims made by John Preskill, Aram Harrow, Scott Aaronson, Dave Bacon, and Boaz Barak.
gilkalai.wordpress.com/2025/02/26/q...

Sergey, is the stronger claim of MZM based topological qubit, gives new avenues to check the concerns regarding data manipulation and data selection?

What you say makes sense: Perhaps we can check if we have genuine qubits and even get some information on their quality by repeated measurements without verifying the MZM claim directly. (Perhaps this can support the MZM claim indirectly.) Alas, I dont understand the technical issues well enough.

Re try: some experimental claims are of the form "(*) If A then B", where B is a system representing a "topological qubit" and A asserts that certain subsystems are Majorana zero modes. There are 1) doubts about "A", 2) claims of insufficient data, 3) doubts on (*).

Dear Barbara, in the Microsoft endeavor, some experimental claims are of the form "(*) If A then B", where B is a system representing a "topological qubit" and B is subsystems representing Majorana zero modes. There are 1) doubts about "B", 2) claims of insufficient data, 3) doubts on *.

Majorana Zero Modes and Topological Qubits 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 …

The post explains a "no go" approach for Majorana zero modes:

Is it the case that samples from states demonstrating Majorana zero modes on a NISQ computer goes (for large numbers of qubits) beyond the Kalai-Kindler LDP complexity class?

gilkalai.wordpress.com/2025/02/21/m...

But does the paper (and/or the earlier arXiv preprint) claim "topological qubit"?

Hi Sergey,
It looks that they claim creating "the first topological qubit" which is (as far as I know, please correct me if I'm wrong) something that goes beyond "just" Majorana zero modes. Is this correct? (That they went a step further?) Or is it the case that they claim MZM as earlier papers?

Robert Alicki, Michel Dyakonov, Leonid Levin, Oded Goldreich, and Others – A Summary of Some Skeptical Views On Quantum Computing. 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 …

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 others.

gilkalai.wordpress.com/2025/02/17/r...

DQC, The slang "is used to describe someone who intentionally engages in savage or hostile behavior, particularly in a verbal or online setting." However, if you follow what I write in these two posts and in my twenty years of qc research and debates, my primary massage is quite the opposite.

Roadmap for the Debate about Quantum Computers 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 question if quantum computing is possible is among the most fascinating scientific questions of our time and the debate on this question is as old as the field itself.
I present a roadmap for the interesting debate from my perspective.

gilkalai.wordpress.com/2025/02/11/r...

There is no violence whatsoever. The roadmap post gives arguments and counterarguments and attempts to describe this lively debate. The assertions post present assertions emerging from my research, and my main purpose is to make them as clear as possible.

Seven Assertions about Quantum Computing. 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.

Seven assertions about quantum computing that arose in my research. I will gladly clarify or elaborate on them and I welcome questions and remarks.
gilkalai.wordpress.com/2025/02/05/s...