Foundations of Mathematics: an Optimistic Message

Stephen G. Simpson ()
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Stephen G. Simpson: Vanderbilt University

Chapter Chapter 20 in The Legacy of Kurt Schütte, 2020, pp 401-414 from Springer

Abstract: Abstract Historically, mathematics has often been regarded as a role model for all of science—a paragon of abstraction, logical precision, and objectivity. The 19th and early 20th centuries saw tremendous progress. The great mathematician David Hilbert proposed a sweeping program whereby the entire panorama of higher mathematical abstractions would be justified objectively and logically, in terms of finite processes. But then in 1931 the great logician Kurt Godel published his famous incompleteness theorems, leading to an era of confusion and skepticism. In this talk I show how modern foundational research has opened a new path toward objectivity and optimism in mathematics.1

Date: 2020
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DOI: 10.1007/978-3-030-49424-7_20

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