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Sergei Tabachnikov

Sergei Tabachnikov is a professor of mathematics at Penn State University and is the Director of the MASS (Mathematics Advanced Study Semesters) program at Penn State. His research interests include Geometry, Topology, and Dynamical Systems; one of his favorite topics is mathematical billiards. In 2013-15, he is serving as the Deputy Director of ICERM (Institute for Computational and Experimental Mathematics) at Brown University. He (co)authored several books, including Mathematical Omnibus, a collection of 30 lectures on classical mathematics. In 1988-90, Sergei headed the mathematical section of Kvant (Quantum) magazine, a Russian monthly on physics and mathematics for high school and college students.

 Sergei Tabachnikov

 

"Equiareal triangulations of a square": If a square is partitioned into triangles of equal areas then the number of these triangles is necessarily even. This theorem, which is only about 40 years old, has a surprisingly non-trivial proof that involves combinatorial topology and number theory. I shall present the proof, describe the history of the problem and mention various related results and conjectures.

 

"Proofs (not) from The Book": According to Erdös, God keeps the most elegant proof of each mathematical result in "The Book". Many mathematicians have their own private collections of "book proofs". In fact, such a collection, and a highly successful one, was published by M. Aigner and G. Ziegler. I shall describe several proofs not included in the Aigner and Ziegler book that, in my opinion, are serious contenders for inclusion in The Book.