Overview

In 1900 David Hilbert (1862-1943), one of the acknowledged leaders of pure mathematics at the turn of the century, identified what he considered to be the most important problems facing contemporary mathematicians at an address to the Second International Congress of Mathematicians. While some of the questions concerned purely technical issues, a number addressed the foundations of mathematics. These led to major changes in the philosophy of mathematics and ultimately to the development of digital computers and artificial intelligence.

Background

The nineteenth century was a period of restructuring in mathematics. Once considered a study of self-evident truths about quantity and space, the paradoxes of set theory and the discovery of non-Euclidean geometries and generalized kinds of numbers motivated mathematicians to reexamine the most fundamental ideas in each area of mathematics. Many mathematicians thought that...