Monthly Archives: December 2008

Can Category Theory Serve as the Foundation of Mathematics?

Usually the foundation of mathematics is thought of as having two pillars: mathematical logic and set theory.  We briefly discussed mathematical logic and the foundation of mathematics in the story of Gödel, Brouwer, and Hilbert. The story of set theory … Continue reading

Posted in What is Mathematics | Tagged | 12 Comments

Gödel, Hilbert and Brouwer

Is mathematics a consistent theory? Or, rather, is there a danger of finding a correct mathematical proof for a false statement like “0 = 1”?  These questions became quite relevant at the end of the nineteenth century, when some mathematical … Continue reading

Posted in What is Mathematics | Tagged , | 2 Comments

A Diameter problem (7): The Best Known Bound

  Our Diameter problem for families of sets Consider a family of subsets of size d of the set N={1,2,…,n}. Associate to a graph as follows: The vertices of  are simply the sets in . Two vertices and are adjacent if . … Continue reading

Posted in Combinatorics, Convex polytopes | Tagged , | 1 Comment