Monthly Archives: March 2019

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

Posted on March 31, 2019 by Gil Kalai

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 Economics, Open discussion, Rationality | Tagged | 11 Comments

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

Posted on March 26, 2019 by Gil Kalai

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 | 40 Comments

Danny Nguyen and Igor Pak: Presburger Arithmetic Problem Solved!

Posted on March 22, 2019 by Gil Kalai

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 , , , , , , , , | 3 Comments

TYI38 Lior Kalai: Monty Hall Meets Survivor

Posted on March 18, 2019 by Gil Kalai

For breaking news, scroll down. Lior Kalai: Survivor Meets the Monty Hall Puzzle We start with the classical question and go on with a new version contributed by my son Lior. Update: A few brief comments on the original problem … Continue reading →

Posted in personal, Probability, Riddles, Test your intuition, Women in science | Tagged , , , | 5 Comments

News on Fractional Helly, Colorful Helly, and Radon

Posted on March 15, 2019 by Gil Kalai

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 , , , , , , , , , , | 3 Comments

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

Posted on March 9, 2019 by Gil Kalai

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 | 18 Comments

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

Posted on March 7, 2019 by Gil Kalai

  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 , | 8 Comments

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

Posted on March 4, 2019 by Gil Kalai

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 | 13 Comments

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

Posted on March 2, 2019 by Gil Kalai

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 →

Posted in Combinatorics, Computer Science and Optimization, Teaching, Updates | Tagged , | Leave a comment