Adam M. Goyt will be speaking on the Banach-Tarski Paradox at Math Seminar

Adam M. Goyt will be speaking on the Banach-Tarski Paradox at Math Seminar

Wednesday, Jan. 17 | 4-5 p.m. | Bridges 268

Abstract: The Banach-Tarski Paradox says that one can divide a three-dimensional sphere into a finite number of pieces and reassemble them to form two spheres, each the same size as the original one. This incredibly counter-intuitive theorem has interested mathematicians since its publication in 1924. The proof of the Banach-Tarski paradox requires the controversial Axiom of Choice, uses the fact that there are sets of points whose measure cannot be determined, and depends heavily on properties of infinity. We will discuss these challenging parts of the proof, and discuss some theoretical physics that may give evidence of the Banach-Tarski paradox in the real world.