David Hilbert

David Hilbert

David Hilbert was a German mathematician and one of the most influential and universal mathematicians of the 19th and early 20th centuries.

David Hilbert was a German mathematician and one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and foundations of mathematics (particularly proof theory). Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.

In 1892 Schwarz moved from Göttingen to Berlin to occupy Weierstrass's chair and Klein wanted to offer Hilbert the vacant Göttingen chair. However Klein failed to persuade his colleagues and Heinrich Weber was appointed to the chair. Klein was probably not too unhappy when Weber moved to a chair at Strasbourg three years later since on this occasion he was successful in his aim of appointing Hilbert. So, in 1895, Hilbert was appointed to the chair of mathematics at the University of Göttingen, where he continued to teach for the rest of his career.

Hilbert's eminent position in the world of mathematics after 1900 meant that other institutions would have liked to tempt him to leave Göttingen and, in 1902, the University of Berlin offered Hilbert Fuchs's chair. Hilbert turned down the Berlin chair, but only after he had used the offer to bargain with Göttingen and persuade them to set up a new chair to bring his friend Minkowski to Göttingen.

At the time Klein received these two letters from Hilbert and Gordan, Hilbert was an assistant lecturer while Gordan was the recognised leading world expert on invariant theory and also a close friend of Klein's. However Klein recognised the importance of Hilbert's work and assured him that it would appear in the Annalen without any changes whatsoever, as indeed it did.

An extract from Hilbert's Preface to Zahlbericht is quote 7 in our collection Quotes by and about Hilbert at THIS LINK.

Hilbert's work in integral equations in about 1909 led directly to 20th-century research in functional analysis (the branch of mathematics in which functions are studied collectively). This work also established the basis for his work on infinite-dimensional space, later called Hilbert space, a concept that is useful in mathematical analysis and quantum mechanics. Making use of his results on integral equations, Hilbert contributed to the development of mathematical physics by his important memoirs on kinetic gas theory and the theory of radiations.

Timeline

1934

In 1934 and 1939 two volumes of Grundlagen der Mathematik T were published which were intended to lead to a 'proof theory', a direct check for the consistency of mathematics.

1899

He published Grundlagen der Geometrie in 1899 putting geometry in a formal axiomatic setting.

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Michael Rowan-Robinson
October 27, 2020
the Guardian
John Barrow speaking in New York after being awarded the 2006 Templeton prize for his writings about the relationship between life and the universe. Photograph: UPI/Alamy Stock Photo
Evelyn Lamb
October 17, 2019
Scientific American Blog Network
The problems shaping modern mathematics

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