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

Posted in Combinatorics, What is Mathematics | Tagged | 5 Comments

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 , , , | 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

Posted in Computer Science and Optimization, Number theory, Open discussion, Philosophy, Updates, What is Mathematics | 15 Comments

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

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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

Posted in Art, Poetry, What is Mathematics | Tagged | 4 Comments

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

Posted in Teaching, What is Mathematics | Tagged , | 16 Comments

Ulam and The Future of Mathematics

Ulam was scheduled to give a talk at the University of Chicago titled “The future of mathematics.” Stanislaw Ulam was a rather famous mathematician and a major player in building the H-bomb, so a large audience gathered.

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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 , | 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 Navier-Stokes equation and he suggests blogs as a way of scaling up scientific conversation. Michael is writing … Continue reading

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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

Posted in Philosophy, What is Mathematics | Tagged | 7 Comments