Monthly Archives: July 2009

The Polynomial Hirsch Conjecture – How to Improve the Upper Bounds.

Posted on July 30, 2009 by Gil Kalai

I can see three main avenues toward making progress on the Polynomial Hirsch conjecture. One direction is trying to improve the upper bounds, for example,  by looking at the current proof and trying to see if it is wasteful and if so where … Continue reading →

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 14 Comments

The Polynomial Hirsch Conjecture, a Proposal for Polymath3 (Cont.)

Posted on July 28, 2009 by Gil Kalai

The Abstract Polynomial Hirsch Conjecture A convex polytope is the convex hull of a finite set of points in a real vector space. A polytope can be described as the intersection of a finite number of closed halfspaces. Polytopes have … Continue reading →

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 5 Comments

How to Debate Beauty

Posted on July 25, 2009 by Gil Kalai

   Who is the most beautiful queen of cards? Opinions vary.  From Gina Says part 2 How to debate Beauty [cosmic variance. Gina Says: May 10th, 2007 at 6:18 am ] The issue of beauty and physics is quite prominent … Continue reading →

Posted in Gina Says | 13 Comments

Gina Says Part two

Posted on July 23, 2009 by Gil Kalai

Download the second part of my book “Gina Says.” Link to the post with the first part.       “Gina Says,” Adventures in the Blogosphere String War selected and edited by Gil Kalai   Praise for “Gina Says”    After having … Continue reading →

Posted in Blogging, Controversies and debates, Gina Says | 15 Comments

A Proof by Induction with a Difficulty

Posted on July 22, 2009 by Gil Kalai

  The time has come to prove that the number of edges in every finite tree is one less than the number of vertices (a tree is a connected graph with no cycle). The proof is by induction, but first you need … Continue reading →

Posted in Teaching, What is Mathematics | Tagged , | 17 Comments

What can the Second Prize Possibly be?

Posted on July 21, 2009 by Gil Kalai

You are guaranteed to win one of the following five prizes, the letter says. (And it is completely free! Just 6 dollars shipping and handling.) a) a high-definition huge-screen TV, b) a video camera, c) a yacht, d) a decorative … Continue reading →

Posted in Mathematics to the rescue, Rationality | Tagged , , | 7 Comments

The Polynomial Hirsch Conjecture: A proposal for Polymath3

Posted on July 17, 2009 by Gil Kalai

This post is continued here.  Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a d-polytope with n vertices  facets has diameter at most n-d. We devoted several … Continue reading →

Posted in Convex polytopes, Open discussion, Open problems | Tagged , , , | 38 Comments

Alarming Developments In Tel Aviv University

Posted on July 13, 2009 by Gil Kalai

Update (July 24): A detailed new article in Hebrew and English. Dr. Leora Meridor, who replaced  Dov Lautman in March (just four months ago)  as chair of TAU’s executive council is quoted saying: ” I’d give him (Zvi Galil) a list … Continue reading →

Posted in Academics, Controversies and debates | Tagged , | 2 Comments

Vitali Fest

Posted on July 12, 2009 by Gil Kalai

Last week I took part in a lovely and impressive conference on the state of geometry and functional analysis, celebrating Vitali Milman’s 70th birthday. The conference started in Tel Aviv, continued at the Dead Sea, and returned to Tel Aviv. I gave a … Continue reading →

Posted in Conferences | 5 Comments

Test Your Intuition (7)

Posted on July 8, 2009 by Gil Kalai

Consider the following game: you have a box that contains one white ball and one black ball. You choose a ball at random and then return it to the box. If you chose a white ball then a white ball is added to … Continue reading →

Posted in Probability, Test your intuition | Tagged | 26 Comments