David Hilbert, 1862 - 1943, was German, and is considered one of the greatest mathematicians ever, leaving a broad legacy in mathematics, physics and philosophy.

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German

Mathematics

Invariant theory, axiomatization of geometry, Hilbert spaces, functional analysis, applications to Physics, philosophy

Lobachevsky Prize, 1903

Bolyai Prize, 1910

Foreign Member of the Royal Society

Senior lecturer, University of Königsberg, 1886 - 1895.

Professor of Mathematics, University of Göttingen, which in his time became the leading mathematics institution of the world. Many of his 69 doctorate students became famous in their turn, including his assistant John Von Neumann, Hermann Weyl and Otto Blumenthal.

Editor of *Mathematische Annalen*, 1902 - 1939, a high-profile journal.

*Grundlagen der Geometrie*, 1899, in which Hilbert proposes his formal set (aka Hilbert's axioms) to replace Euclid's axioms.

A list of 23 unsolved problems at the International Congress of Mathematicians in Paris, 1900. This list had a great impact and influence on mathematical thinking in the 20th century, and some continue to intrigue and puzzle.

*Principles of Mathematical Logic*, 1928, co-authored with Wilhelm Ackermann.

*Grundlagen der Mathematik*, two volumes (1934 and 1939), co-authored with Paul Bernays.

*The Foundations of Physics*, 1915, an axiomatic derivation of he field equations of General Relativity.

Hilbert's axioms

Hilbert's basis theorem

Hilbert's problems

Hilbert's program

Einstein-Hilbert action

Hilbert space

Hilbert's problem set was instrumental in the establishment and development of the *formalist* school.

He developed important tools, and was instrumental in developing the field of mathematical physics. He was a founder of proof theory, mathematical logic, and metamathematics.

Although primarily known as a mathematician, Hilbert made significant contributions to physics. There is evidence that Hilbert produced a General Relativity theory of his own, and influenced Albert Einstein greatly. Hilbert graciously made no claim to the theory. Hilbert also made contributions to quantum mechanics, and influenced Weyl and von Neumann in their work on Heisenberg's matrix mechanics, and Schrödinger's wave equation. Hilbert space

(Biographies of famous scientists no. 87)

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1883 - 1946

John Maynard Keynes was an English macroeconomist, whose ideas revolutionised modern economic thinking, and are still used as the basis of many western capitalist economies.

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