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Scientist

David Hilbert

1862–1943 · mathematics, mathematical physics, functional analysis, number theory, mathematical logic

David Hilbert is one of the greatest mathematicians in history, whose ideas defined the face of modern mathematics and laid the foundation for the mathematical apparatus of quantum mechanics. He developed the theory of Hilbert spaces, formulated the famous 23 problems that became a program for the development of mathematics in the 20th century, and made fundamental contributions to invariant theory, algebraic number theory, and mathematical logic.

Biography

Born in Königsberg (now Kaliningrad), he studied and worked at the University of Königsberg, where he became friends with Hermann Minkowski. From 1895, he was a professor at the University of Göttingen, which under him became a world center of mathematics. Among his students and colleagues were John von Neumann, Hermann Weyl, Emmy Noether. He was a laureate of the Lobachevsky Prize and many other awards. His scientific school became legendary.

Key discoveries

Hilbert space: an abstract vector space with an inner product, which became the mathematical foundation of quantum mechanics (wave function as a state vector).
Hilbert's problems: a list of 23 unsolved problems presented in 1900 that determined the main directions of mathematical research for decades to come (some have been solved, others are still open).
Invariant theory and the basis theorem: proof of the finite generation of invariants, which laid the foundation for modern algebraic geometry.

💡 Hilbert lectured slowly and often repeated difficult parts so that even the slowest students could understand the material. On his deathbed, he supposedly said about his 23 problems: 'Put me close to the mathematics department at the cemetery — maybe I'll resurrect.'

"He asserted that we must know, and we will know."

Concepts

Hilbert space quantum entanglement quantum measurement superposition uncertainty principle

Laws

spectral theorem

Scientists

Alain Aspect Erwin Schrödinger David Deutsch Louis de Broglie John Stewart Bell Leo Esaki Niels Bohr Serge Haroche

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