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Topic Archive: constructive mathematics

Computational Logic SeminarThursday, September 29, 20164:00 pmGraduate Center, rm. 8400

Sam Sanders

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.