David Hilbert

Overview

Hilbert spent most of his career at Göttingen, which he made the centre of mathematics until the university was emptied by the Nazi government in 1933. The Foundations of Geometry, published in 1899, rebuilt Euclid on a complete and explicit set of axioms, supplying the assumptions about order and continuity that Euclid had used silently, and treating the axioms as defining whatever objects satisfy them. At the 1900 congress in Paris he set out a list of open problems, twenty-three in the published version, which directed a great deal of the century's work. His programme aimed to formalise all of mathematics and then prove, by finite and uncontroversial reasoning, that no contradiction could be derived; Gödel's theorems of 1931 showed that this cannot be done in the form intended. Start with The Foundations of Geometry, which is free on Project Gutenberg and readable with school geometry.

Where to start reading

• The Foundations of Geometry 1899

  A complete axiom system for Euclidean geometry, with the independence and consistency of the axioms examined directly.

  Read it on Project Gutenberg

• Mathematical Problems 1900

  The address to the International Congress of Mathematicians listing the open problems that shaped much of twentieth-century mathematics.

Part of

• Formalism and the Hilbert programme
• Euclidean geometry

Sources

1. David Hilbert MacTutor History of Mathematics
2. David Hilbert Wikipedia
3. Hilbert's Program Stanford Encyclopedia of Philosophy