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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
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
Posted in Probability, Riddles, Test your intuition
Tagged Lior Kalai, Monty Hall problem, Survivor
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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
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
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
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.
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
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 Brad Rodgers, Dan Romik, Don Zagier, Ken Ono, Larry Rolen, Michel Griffin, polymath15, Terry Tao, Zeta function
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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 g-conjecture, J Scott Provan, Karim Adiprasito, Leonid Gurvits, Lou Billera
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