The unreasonable effectiveness of Nonstandard Analysis.
Department of Mathematics, Ghent University
Nonstandard Analysis (NSA) was introduced around 1965 by Robinson as a formalization of the intuitive infinitesimal calculus which is in use to date in most of physics and historically in mathematics until the advent of Weierstrass’ epsilon-delta framework. Famous people like Connes and Bishop have derided NSA for its alleged utter lack of computational/effective/constructive content. In this talk I show that every theorem of ‘pure’ NSA can be (equivalently) converted to a theorem of computable mathematics. In many cases, the resulting theorem is even constructive in the sense of Bishop.
Sam Sanders finished his PhD in 2010 at Ghent University, under the supervision of Andreas Weiermann and Chris Impens, and now holds a postdoctoral position there. He studies analysis and the foundations of mathematics, doing work in reverse mathematics using nonstandard analysis, proof theory, and computability theory.