Textbook of AI

1862–1943, Mathematician

Also known as: D. Hilbert

David Hilbert was the dominant German mathematician of the early twentieth century. His 1900 address to the International Congress of Mathematicians in Paris, where he posed twenty-three open problems, set much of the agenda for mathematical research in the century that followed. Two of his enterprises bear directly on the foundations of computer science and AI.

The first is Hilbert's programme, his proposal that mathematics could be set on a finitely specifiable, complete and consistent axiomatic foundation. The programme was undermined in 1931 by Kurt Gödel's incompleteness theorems, which showed that any consistent formal system rich enough to express arithmetic must contain true statements it cannot prove.

The second is the Entscheidungsproblem (decision problem), posed by Hilbert and Wilhelm Ackermann in their 1928 Grundzüge der theoretischen Logik: is there an effective procedure that, given any statement in first-order logic, decides whether it is provable? Alan Turing answered this in the negative in 1936, using his model of computation, the Turing machine, to show that the problem is undecidable. Alonzo Church reached the same conclusion independently using the lambda calculus. The pair of papers founded computability theory and gave AI its mathematical model of what an algorithm is.

Hilbert spent almost his entire career at the University of Göttingen, which under his leadership became the world centre of mathematics until the rise of the Nazis dismantled the faculty in 1933. His tombstone bears his motto: Wir müssen wissen, wir werden wissen ("We must know , we will know").