Experimental Mathematics, Armchair Physics

Abstract

"Philosophers have traditionally classified mathematical knowledge as 'a priori' and scientific knowledge as 'a posteriori,'" Baler says. "In other words, mathematics can be done without leaving one's armchair, while physics cannot. In this lecture I challenge both sides of this traditional picture. On the one hand, are there such things as 'mathematical experiments' and what kind of role might they play in mathematics? On the other hand, can conclusions be justifiably reached about the nature of the physical world that do not depend on observation or experiment?" The lecture is intended for a general audience and no specific mathematical or scientific background is presupposed.