Physical Reasoning in Mathematics

Friday, January 27, 2012 - 15:00 to 15:50
Speaker Information
Mark Levi
Penn State University

Abstract or Additional Information

Physics often provides mathematics not only with a problem, but also with the idea of a solution. Some calculus problems can be solved more quickly without calculus, by using physics instead. Quite a few theorems which may seem somewhat mysterious become completely obvious when given a proper physical incarnation. This is the case for some "elementary" theorems (the Pythagorean Theorem, Pappus' theorems, some trig identities, Euler's formula V-E+F=2, and more) and for some less elementary ones: Noether's theorem on conserved quantities, the preservation of Poincaré's integral invariants, the Gauss-Bonnet theorem, the Riemann Mapping Theorem, Green's theorem, Moser's theorem on Jacobians, the uniformization theorem, and more (no familiarity with any of these is assumed). I will describe a miscellaneous sampling of problems according to the audience's preferences.

Research Area