Monthly Archives: June 2013

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

Posted on June 19, 2013 by Gil Kalai

…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 , , , , , | 50 Comments

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

Posted on June 19, 2013 by Gil Kalai

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

Posted on June 11, 2013 by Gil Kalai

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