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Category Archives: What is Mathematics
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
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
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
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
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
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.
“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
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
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
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