Author Archives: Gil Kalai

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

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Test Your Intuition (21): Auctions

You run a single-item sealed bid auction where you sell an old camera. There are three bidders and the value of the camera for each of them is described by a certain (known) random variable: With probability 0.9 the value … Continue reading

Posted in Economics, Games, Test your intuition | Tagged , , | 4 Comments

Oz’ Balls Problem: The Solution

A commentator named Oz proposed the following question: You have a box with n red balls and n blue balls. You take out each time a ball at random but, if the ball was red, you put it back in the box and take out … Continue reading

Posted in Probability, Test your intuition | Tagged , , , | 1 Comment

Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun

            Yeshu Kolodni and Lord Kelvin The question In 1862, the physicist William Thomson (who later became Lord Kelvin) of Glasgow published calculations that fixed the age of Earth at between 20 million and 400 … Continue reading

Posted in Geology, Physics, Test your intuition | 4 Comments