Monthly Archives: May 2009

Some Philosophy of Science

Posted on May 31, 2009 by Gil Kalai

The Bayesian approach to the philosophy of science was developed in the first half of the twentieth century. Karl Popper and Thomas Kuhn are twentieth-century philosophers of science who later proposed alternative approaches. It will be convenient to start with … Continue reading →

Posted in Philosophy, Probability | 14 Comments

A Workshop for Advanced Undergraduate Students, Sept 6-17 2009

Posted on May 27, 2009 by Gil Kalai

סדנא לתלמידי בוגר מצטיינים במתמטיקה מכון איינשטיין למתמטיקה, האוניברסיטה העברית בירושלים יום א’ י”ז אלול – יום ה’ כ”ח אלול תשס”ט 6-17/9/09 המכון למתמטיקה של האוניברסיטה העברית מזמין תלמידי מתמטיקה מצטיינים המסיימים שנה ב’ או ג’ של לימודיהם במוסדות להשכלה … Continue reading →

Posted in Updates | 1 Comment

Answer to Test Your Intuition (3)

Posted on May 27, 2009 by Gil Kalai

Question: Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in . Answer: Taking to be all points in the solid … Continue reading →

Posted in Geometry, Test your intuition | Tagged | 2 Comments

Ulam and The Future of Mathematics

Posted on May 26, 2009 by Gil Kalai

Ulam was scheduled to give a talk at the University of Chicago titled “The future of mathematics.” Stanislaw Ulam was a rather famous mathematician and a major player in building the H-bomb, so a large audience gathered.

Posted in Taxi-and-other-stories, What is Mathematics | Tagged | Leave a comment

How Large can a Spherical Set Without Two Orthogonal Vectors Be?

Posted on May 22, 2009 by Gil Kalai

The problem Witsenhausen’s Problem (1974): Let be a measurable subset of the -dimensional sphere . Suppose that does not contain two orthogonal vectors. How large can the -dimensional volume of be?   A Conjecture Conjecture: The maximum volume is attained … Continue reading →

Posted in Open problems | 4 Comments

Extremal Combinatorics VI: The Frankl-Wilson Theorem

Posted on May 21, 2009 by Gil Kalai

Rick Wilson The Frankl-Wilson theorem is a remarkable theorem with many amazing applications. It has several proofs, all based on linear algebra methods (also referred to as dimension arguments). The original proof is based on a careful study of incidence … Continue reading →

Posted in Combinatorics | Tagged , | 20 Comments

Recent and Future Excitements

Posted on May 20, 2009 by Gil Kalai

It is very hectic around here and on top of the eight or so regular research seminars at math (and quite a few more at CS) we have many visitors as school terms at the US are over. A week … Continue reading →

Posted in Updates | Leave a comment

The Cap-Set Problem and Frankl-Rodl Theorem (C)

Posted on May 18, 2009 by Gil Kalai

Update: This is a third of three posts (part I, part II) proposing some extensions of the cap set problem and some connections with the Frankl Rodl theorem. Here is a post presenting the problem on Terry Tao’s blog (March 2007). Here … Continue reading →

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

Ehud Friedgut: Murphy’s Law of Breastfeeding Twins

Posted on May 17, 2009 by Gil Kalai

This post is authored by Ehud Friedgut. Congratulations to Keren, Ehud and Michal for the birth of Shiri and Hillel! Murphy’s law of breastfeeding twins, like all of Murphy’s laws, is supported by strong empirical evidence. The twins’ feeding rhythm … Continue reading →

Posted in Guest blogger, Rationality | Tagged | 10 Comments

The Amitsur-Levitzki Theorem for a Non Mathematician.

Posted on May 12, 2009 by Gil Kalai

Yaacov Levitzki The purpose of this post is to describe the Amitsur-Levitzki theorem: It is meant for people who are not necessarily mathematicians. Yet they need to know two things. The first is what matrices are. Very briefly, matrices are rectangular arrays … Continue reading →

Posted in Algebra | Tagged , | 8 Comments