Author Archives: Gil Kalai

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

In 2006, the popular science magazine “Galileo” prepared a special issue devoted to milestones in the History of several areas of science and Nati Linial and me wrote the article about mathematics Ten milestones in the history of mathematics (in … Continue reading

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

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 , , , , , , , , | 1 Comment

TYI38 Lior Kalai: Monty Hall Meets Survivor

Before moving to our riddle Breaking news: (added March 20, 2019) I am very happy to report that yesterday, March 19, 2019, Karen Uhlenbeck was awarded the 2019 Abel prize “for her pioneering achievements in geometric partial differential equations, gauge … Continue reading

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News on Fractional Helly, Colorful Helly, and Radon

My 1983 Ph D thesis was on Helly-type theorems which is an exciting part of discrete geometry and, in the last two decades, I have had an ongoing research project with Roy Meshulam on topological Helly-type theorems. The subject found … Continue reading

Posted in Combinatorics, Convexity | Tagged , , , , , , , , , , | 2 Comments

8866128975287528³+(-8778405442862239)³+(-2736111468807040)³

Update: The result was achieved by Andrew Booker from Bristol. Here is the preprint Cracking the problem with 33. It is a notoriously difficult open problem which integers can be written as the sum of three integer cubes.  Such integers … Continue reading

Posted in Number theory | Tagged | 16 Comments

Test Your Intuition (or simply guess) 37: Arithmetic Progressions for Brownian Motion in Space

  Consider a Brownian motion in three dimensional space. 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.)   A 2-D picture; In … Continue reading

Posted in Probability, Test your intuition | Tagged , | 7 Comments

Test Your Intuition (or knowledge, or programming skills) 36

How much is   The product ranges over all primes. In other words, Just heard it from Avinoam Mann.  

Posted in Number theory, Test your intuition | Tagged | 10 Comments

Bob Sedgewick’s Free Online Courses on Analysis of Algorithms and Analytic Combinatorics.

Philippe Flajolet 1948-2011   I am  happy to forward the announcement on two free online courses (Mooks) by Bob Sedgewick  Analysis of Algorithms and Analytic Combinatorics. Analysis of Algorithms  page provides access to online lectures, lecture slides, and assignments for … Continue reading

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Dan Romik Studies the Riemann’s Zeta Function, and Other Zeta News.

Updates to previous posts: Karim Adiprasito expanded in a comment to his post on the g-conjecture on how to move from vertex-decomposable spheres to general spheres. Some photos were added to the post: Three pictures. Dan Romik on the Zeta … Continue reading

Posted in Number theory, Updates | Tagged , , , , , , , , | 2 Comments

Karim Adiprasito: The g-Conjecture for Vertex Decomposible Spheres

J Scott Provan (site) The following post was kindly contributed by Karim Adiprasito. (Here is the link to Karim’s paper.) Update: See Karim’s comment on the needed ideas for extend the proof to the general case. See also  in the … Continue reading

Posted in Combinatorics, Convex polytopes, Geometry, Guest blogger | Tagged , , , , | 9 Comments