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 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
 Is HeadsUp Poker in P?
Top Posts & Pages
 Timothy Chow Launched Polymath12 on Rota Basis Conjecture and Other News
 Thilo Weinert: Transfinite Ramsey Numbers
 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
 Proof By Lice!
 The seventeen camels riddle, and Noga Alon's camel proof and algorithms
 Galvin's Proof of Dinitz's Conjecture
 Itamar Pitowsky: Probability in Physics, Where does it Come From?
 In how many ways you can chose a committee of three students from a class of ten students?
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Category Archives: What is Mathematics
Proof By Lice!
From camels to lice. (A proof promised here.) Theorem (Hopf and Pannwitz, 1934): Let be a set of points in the plane in general position (no three points on a line) and consider line segments whose endpoints are in . Then … Continue reading
Why is Mathematics Possible: Tim Gowers’s Take on the Matter
In a previous post I mentioned the question of why is mathematics possible. Among the interesting comments to the post, here is a comment by Tim Gowers: “Maybe the following would be a way of rephrasing your question. We know … Continue reading
Posted in Open discussion, Philosophy, What is Mathematics
Tagged Foundations of Mathematics, Open discussion, Philosophy, Tim Gowers
23 Comments
Why is mathematics possible?
Spectacular advances in number theory Last weeks we heard about two spectacular results in number theory. As announced in Nature, Yitang Zhang proved that there are infinitely many pairs of consecutive primes which are at most 70 million apart! This is a sensational achievement. … Continue reading
Fundamental Examples
It is not unusual that a single example or a very few shape an entire mathematical discipline. Can you give examples for such examples? I’d love to learn about further basic or central examples and I think such examples serve … Continue reading
Posted in What is Mathematics
15 Comments
Rodica Simion: Immigrant Complex
Rodica Simion immigrated to the United States from Romania. She was a Professor of Mathematices at George Washington University untill her untimely death on January 7, 2000. Her poem “Immigrant complex” appeared in : “Against Infinity”, An Anthology of Contemporary … Continue reading
A Proof by Induction with a Difficulty
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
Polymath1: Success!
“polymath” based on internet image search And here is a link to the current draft of the paper. Update: March 26, the name of the post originally entitled “Polymath1: Probable Success!” was now updated to “Polymath1: Success!” It is now becoming … Continue reading
Posted in Blogging, Combinatorics, What is Mathematics
Tagged Density HalesJewett theorem, polymath1
10 Comments
Mathematics, Science, and Blogs
Michael Nielsen wrote a lovely essay entitled “Doing science online” about mathematics, science, and blogs. Michael’s primary example is a post over Terry Tao’s blog about the NavierStokes equation and he suggests blogs as a way of scaling up scientific conversation. Michael is writing … Continue reading
Posted in Blogging, What is Mathematics
Tagged Blogs, Michael Nielsen, Open science, polymath1, Tim Gowers
5 Comments
Fundamental Impossibilities
An Understanding of our fundamental limitations is among the most important contributions of science and of mathematics. There are quite a few cases where things that seemed possible and had been pursued for centuries in fact turned out to be … Continue reading