David Hilbert

David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. His own discoveries alone would have given him that honor, yet it was his leadership in the field of mathematics throughout his later life that distinguishes him. He held a professorship in mathematics at the University of Göttingen for most of his life.

Miscellaneous talks, essays, and contributions

He put forth a most influential list of 23 unsolved problems at the International Congress of Mathematicians in Paris in 1900. This is generally reckoned the most successful and deeply considered compilation of open problems ever to be produced by an individual mathematician.

Related Topics:
23 unsolved problems - International Congress of Mathematicians - Paris

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Additionally, Hilbert's work anticipated and assisted several advances in the mathematical formulation of quantum mechanics. These include his introduction of Hilbert space, and Hermann Weyl's proof of the mathematical equivalence of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation.

Related Topics:
Mathematical formulation of quantum mechanics - Hilbert space - Hermann Weyl - Werner Heisenberg - Matrix mechanics - Erwin Schrödinger - Wave equation

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His paradox of the Grand Hotel, a meditation on strange properties of the infinite, is often used in popular accounts of infinite cardinal numbers.

Related Topics:
Paradox of the Grand Hotel - Cardinal number

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Hilbert's program

In 1920 he proposed explicitly a research project (in metamathematics, as it was then termed) that became known as Hilbert's program. He wanted mathematics to be formulated on a solid and complete logical foundation. He believed that in principle this could be done, by showing that:

Related Topics:
1920 - Metamathematics - Hilbert's program - Mathematics

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• all of mathematics follows from a correctly-chosen finite system of axioms; and
• that some such axiom system is probably consistent.

There seem to have been both technical and psychological reasons why he formulated this proposal. It affirmed his dislike of what had become known as the ignorabimus, still an active issue in his time in German thought, and traced back in that formulation to Emil du Bois-Reymond.

Related Topics:
Ignorabimus - Emil du Bois-Reymond

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This program is still recognisable in the most popular philosophy of mathematics, amongst working mathematicians that is, usually called formalism. For example, the Bourbaki group adopted a milk-and-water version of it as adequate to the requirements of their twin projects of (a) writing encyclopedic foundational works, and (b) supporting the axiomatic method as a research tool.

Related Topics:
Philosophy of mathematics - Formalism - Bourbaki - Axiomatic method

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Gödel's incompleteness theorem showed, however, in 1931 that Hilbert's grand plan was impossible, as stated. The point 2 cannot in any reasonable way be combined with the point 1, as long as the axiom system is genuinely finitary.

Related Topics:
Gödel's - Incompleteness theorem - 1931 - Finitary

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