The Most Outrageous Conjecture in the World

Donald Knuth, Enrico Bombieri, and Julia Robinson. Ten years ago I asked a question on MathOverflow about The most outrageous (or ridiculous) conjectures in mathematics. It led to a nice list of ma…

Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans

With Danny and Sharon Kleitman and Michel Goemans at the MIT Endicott house. Update: There are many reactions and emerging details on the new 700 or so papers released by Open AI. On Persiflage the…

Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans

With Danny and Sharon Kleitman and Michel Goemans at the MIT Endicott house. Update: There are many reactions and emerging details on the new 700 or so papers released by Open AI. On Persiflage the…

Quantum Computers and Applied Mathematics at Brown University

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…

Jeff Fest: Probabilistic Combinatorics at Rutgers

Greetings from Providence! Next week there will be a conference at Rutgers University in honor of Jeff Kahn. Jeff is a great mathematician whose contributions span all areas of combinatorics. He ha…

Tobias Boege and Geva Yashfe: Recognizing Algebraic Matroids Is Undecidable

Algebraic Matroids are Undecidable Tobias Boege and Geva Yashfe have posted a remarkable paper, Recognition of algebraic matroids is undecidable. It brings together matroid theory, algebraic geomet…

“Be a Grothendieck!”—On AI and Mathematics

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’…

Alef’s corner: AI and Percolation

Jesús A. De Loera, Ethan X. Fang, Shengtao Guo, Junwei Lu, and Hailun Zheng Proved the Simplex–Cube...

Shana Tova Shana Tova (happy new Jewish year) to all our readers! We have just returned to Tel Aviv from  the beautiful city of Tiberias, on the Sea of Galilee. The Simplex cube conjecture The simp…

Overtaken

In the early to mid-1970s, my university classmate Ariel Rubinstein initiated a weekend hike from Jerusalem to the Dead Sea. A group of us left Jerusalem on Friday night, planning to reach the Dead…

Test Your Intuition 59 : The Conclave Process

  When the papacy becomes vacant, a new pope is elected through a procedure known as the conclave. Cardinal-electors from around the world gather in the Sistine Chapel and vote in successive r…

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…

Polymath Plus AI

This post was written together with Nissan Hajaj and Ido Kaminer.  Update (June 26,2026):  The problem for the first project has now been resolved.  Update (June, 26, 2926): For all projects (curre…

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…

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…