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- To cheer you up in difficult times 21: Giles Gardam lecture and new result on Kaplansky's conjectures
- To cheer you up in difficult times 5: A New Elementary Proof of the Prime Number Theorem by Florian K. Richter
- What is mathematics (or at least, how it feels)
- The Argument Against Quantum Computers - A Very Short Introduction
- Extremal Combinatorics VI: The Frankl-Wilson Theorem
- Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Yael Tauman Kalai's ICM2018 Paper, My Paper, and Cryptography
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Category Archives: Open discussion
The Polynomial Hirsch Conjecture: Discussion Thread, Continued
Here is a link for the just-posted paper Diameter of Polyhedra: The Limits of Abstraction by Freidrich Eisenbrand, Nicolai Hahnle, Sasha Razborov, and Thomas Rothvoss. And here is a link to the paper by Sandeep Koranne and Anand Kulkarni “The d-step Conjecture is Almost true” – … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Convex polytopes, Hirsch conjecture
16 Comments
The Polynomial Hirsch Conjecture: Discussion Thread
This post is devoted to the polymath-proposal 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 d-polytope with n vertices facets has diameter at most n-d. 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
29 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
7 Comments