Author Archives: Gil Kalai

Lawler-Kozdron-Richards-Stroock’s combined Proof for the Matrix-Tree theorem and Wilson’s Theorem

   David Wilson and a cover of Shlomo’s recent book “Curvature in mathematics and physics” A few weeks ago, in David Kazhdan’s basic notion seminar, Shlomo Sternberg gave a lovely presentation Kirchho ff and Wilson via Kozdron and Stroock. The lecture is based on … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Probability | Tagged , , | 4 Comments

Auction-based Tic Tac Toe: Solution

Reshef, Moshe and Sam The question: (based on discussions with Reshef Meir, Moshe Tennenholtz, and Sam Payne) Tic Tac Toe is played since anciant times. For the common version, where the two players X and O take turns in marking … Continue reading

Posted in Games, Test your intuition | Tagged | 6 Comments

Some old and new problems in combinatorics and geometry

Paul Erdős in Jerusalem, 1933  1993 I just came back from a great Erdős Centennial conference in wonderful Budapest. I gave a lecture on old and new problems (mainly) in combinatorics and geometry (here are the slides), where I presented twenty … Continue reading

Posted in Combinatorics, Geometry, Open problems | Tagged | 4 Comments

The Kadison-Singer Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava

…while we keep discussing why mathematics is possible… The news Adam Marcus, Dan Spielman, and Nikhil Srivastava posted a paper entitled “Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem,” where they prove the 1959 Kadison-Singer conjecture. (We discussed part … Continue reading

Posted in Analysis, Computer Science and Optimization, Physics, Updates | Tagged , , , , , | 30 Comments

Why is Mathematics Possible: Tim Gowers’s Take on the Matter

In a previous post I mentioned the question of why is mathematics possible. Among the interesting comments to the post, here is a comment by Tim Gowers: “Maybe the following would be a way of rephrasing your question. We know … Continue reading

Posted in Open discussion, Philosophy, What is Mathematics | Tagged , , , | 23 Comments

Polymath8: Bounded Gaps Between Primes

Yitang Zhang’s very recent shocking paper demonstrated that bounded gaps between primes occur infinitely often, with the explicit upper bound of 70,000,000 given for this gap. Polymath8 was launched for the dual purpose of learning Zhang’s proof and improving the upper bound … Continue reading

Posted in Mathematics over the Internet, Number theory, Updates | Tagged , | Leave a comment

Joram’s Memorial Conference

Joram Lindenstrauss 1936-2012 This week our local Institute of Advanced Study holds a memorial conference for Joram Lindenstrauss. Joram was an immensely powerful mathematician, in terms of originality and conceptual vision, in terms of technical power, in terms of courage to confront … Continue reading

Posted in Conferences, Obituary | Tagged | 1 Comment

Andriy Bondarenko Showed that Borsuk’s Conjecture is False for Dimensions Greater Than 65!

The news in brief Andriy V. Bondarenko proved in his remarkable paper The Borsuk Conjecture for two-distance sets  that the Borsuk’s conjecture is false for all dimensions greater than 65. This is a substantial improvement of the earlier record (all dimensions … Continue reading

Posted in Combinatorics, Geometry, Open problems | Tagged , , , , | 2 Comments

Why is mathematics possible?

Spectacular advances in number theory Last weeks we heard about two spectacular results in number theory.  As announced in Nature, Yitang Zhang proved that there are infinitely many pairs of consecutive primes which are at most 70 million apart! This is a sensational achievement. … Continue reading

Posted in Computer Science and Optimization, Number theory, Open discussion, Philosophy, Updates, What is Mathematics | 15 Comments

Dan Mostow on Haaretz and Other Updates

Enlightenment at a red traffic light Wolf Prize laureate Prof. George Daniel Mostow made his greatest scientific breakthrough while driving. Haaretz tells the story of how Dan Mostow reached his breakthrough known as Mostow’s rigidity theorem. Congratulations, Dan! French-Isreali Meeting … Continue reading

Posted in Updates | Tagged , | 1 Comment