Author Archives: Gil Kalai

A sensation in the morning news – Yaroslav Shitov: Counterexamples to Hedetniemi’s conjecture.

Two days ago Nati Linial sent me an email entitled “A sensation in the morning news”. The link was to a new arXived paper by Yaroslav Shitov: Counterexamples to Hedetniemi’s conjecture. Hedetniemi’s 1966 conjecture asserts that if and are two … Continue reading

Posted in Combinatorics, Open problems, Updates | Tagged , | 9 Comments

Answer to TYI 37: Arithmetic Progressions in 3D Brownian Motion

Consider a Brownian motion in three dimensional space. We asked (TYI 37) What is the largest number of points on the path described by the motion which form an arithmetic progression? (Namely, , so that all are equal.) Here is … Continue reading

Posted in Combinatorics, Open discussion, Probability | Tagged , , | 1 Comment

The last paper of Catherine Rényi and Alfréd Rényi: Counting k-Trees

A k-tree is a graph obtained as follows: A clique with k vertices is a k-tree. A k-tree with n+1 vertices is obtained from a k-tree with n-vertices by adding a new vertex and connecting it to all vertices of a … Continue reading

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Are Natural Mathematical Problems Bad Problems?

One unique aspect of the conference “Visions in Mathematics Towards 2000” (see the previous post) was that there were several discussion sessions where speakers and other participants presented some thoughts about mathematics (or some specific areas), discussed and argued.  In … Continue reading

Posted in Combinatorics, Conferences, Open discussion, What is Mathematics | Tagged | 1 Comment

An Invitation to a Conference: Visions in Mathematics towards 2000

Let me invite you to a conference. The conference took place in 1999 but only recently the 57 videos of the lectures and the discussion sessions are publicly available. (I thank Vitali Milman for telling me about it.) One novel … Continue reading

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The (Random) Matrix and more

Three pictures, and a few related links. Van Vu Spoiler: In one of the most intense scenes, the protagonist, with his bare hands and against all odds, took care of the mighty Wigner semi-circle law in two different ways. (From … Continue reading

Posted in Combinatorics, People, What is Mathematics | Tagged , , , , , , | 1 Comment

Gothenburg, Stockholm, Lancaster, Mitzpe Ramon, and Israeli Election Day 2019

Lancaster – Watching the outcomes of the Israeli elections (photo: Andrey Kupavskii) Sweden I just came back from a trip to Sweden and the U.K. I was invited to Gothenburg to be the opponent for a Ph. D. Candidate  Malin … Continue reading

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Is it Legitimate/Ethical for Google to close Google+?

Update April 2, 2019: the links below are not working anymore.  Google Plus is a nice social platform with tens of millions participants. I found it especially nice for scientific posts, e.g. by John Baez, Moshe Vardi, or about symplectic … Continue reading

Posted in Combinatorics, Economics, Open discussion, Rationality | Tagged | 9 Comments

10 Milestones in the History of Mathematics according to Nati and Me

Breaking news: David Harvey and Joris Van Der Hoeven. Integer multiplication in time O(nlogn). 2019. (I heard about it from Yoni Rozenshein on FB (חפירות על מתמטיקה); update GLL post. )  _____ Update: There were many interesting comments here and … Continue reading

Posted in Open discussion, What is Mathematics | Tagged | 38 Comments

Danny Nguyen and Igor Pak: Presburger Arithmetic Problem Solved!

Short Presburger arithmetic is hard! This is a belated report on a remarkable breakthrough from 2017. The paper is Short Presburger arithmetic is hard, by Nguyen and Pak. Danny Nguyen Integer programming in bounded dimension: Lenstra’s Theorem Algorithmic tasks are … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Convex polytopes | Tagged , , , , , , , , | 2 Comments