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 Test Your Intuition about the AlonTarsi Conjecture
 Thilo Weinert: Transfinite Ramsey Numbers
 Timothy Chow Launched Polymath12 on Rota Basis Conjecture and Other News
 Proof By Lice!
 The seventeen camels riddle, and Noga Alon’s camel proof and algorithms
 Edmund Landau and the Early Days of the Hebrew University of Jerusalem
 Boolean Functions: Influence, Threshold, and Noise
 Laci Babai Visits Israel!
 Polymath10 conclusion
Top Posts & Pages
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 Extremal Combinatorics IV: Shifting
 Greg Kuperberg: It is in NP to Tell if a Knot is Knotted! (under GRH!)
 Test Your Intuition about the AlonTarsi Conjecture
 Can Category Theory Serve as the Foundation of Mathematics?
 Noise Stability and Threshold Circuits
 Updates and plans III.
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
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Category Archives: Open discussion
The Polynomial Hirsch Conjecture: Discussion Thread
This post is devoted to the polymathproposal about the polynomial Hirsch conjecture. My intention is to start here a discussion thread on the problem and related problems. (Perhaps identifying further interesting related problems and research directions.) Earlier posts are: The polynomial Hirsch … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Hirsch conjecture, Polytopes
115 Comments
The Polynomial Hirsch Conjecture – How to Improve the Upper Bounds.
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 Discussion, Hirsch conjecture
14 Comments
The Polynomial Hirsch Conjecture, a Proposal for Polymath3 (Cont.)
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 Hirsch conjecture, Polymath proposals
5 Comments
The Polynomial Hirsch Conjecture: A proposal for Polymath3
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 dpolytope with n vertices facets has diameter at most nd. We devoted several … Continue reading
An Open Discussion and Polls: Around Roth’s Theorem
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 Cap sets, polymath1, Roth's theorem, Szemeredi's theorem
26 Comments
Is Mathematics a Science?
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 Mathematics, Philosophy of science
5 Comments