Foundations of mathematics: an optimistic message

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 Gödel 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. SLIDE SLIDE Good evening to all. Basically I am a mathematics professor, and my task this evening is to explain something about my research area, mathematical logic and foundations of mathematics. Throughout history, mathematics and logic have been regarded not only as indispensable components of most other sciences, but also as role models for all of science – the most objective and logically perfect of all the sciences. For these reasons, scientists throughout history have thought that it is particularly important to understand the logical structure of mathematics. And that is the need which my research area seeks to fulfill. Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics. This document is the text of my Public Lecture at the National University of Singapore, to be delivered January 6, 2016.