Category Archives: Open discussion

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

Posted on July 28, 2009 by

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

The Polynomial Hirsch Conjecture: A proposal for Polymath3

Posted on July 17, 2009 by

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

An Open Discussion and Polls: Around Roth’s Theorem

Posted on March 25, 2009 by

Suppose that  is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . How does behave? We do not really know. Will it help talking about it? Can we somehow look beyond the horizon and try to guess what … Continue reading →

Posted in Combinatorics, Open discussion, Open problems | Tagged , , , | 24 Comments

Is Mathematics a Science?

Posted on May 25, 2008 by

Many people do not regard mathematics as a science since it does not directly probe our physical reality; some mathematicians even like to think about mathematics as being closer to art, music or literature. But is there really a big … Continue reading →

Posted in Open discussion, Philosophy, What is Mathematics | Tagged , | 4 Comments