Hilbert (name)
Hilbert, in mathematics and related fields, most commonly refers to David Hilbert (1862-1943), a German mathematician. Hilbert was one of the most influential mathematicians of the 19th and 20th centuries. He is known as the founder of formalism, and for his substantial contributions to a wide range of mathematical areas, including mathematical logic, axiomatic geometry, functional analysis, number theory, and the foundations of physics.
His famous "Hilbert's Problems," a list of twenty-three unsolved mathematical problems presented at the International Congress of Mathematicians in 1900, shaped much of the mathematical research of the 20th century. Many of these problems have since been solved, while others remain open to this day.
The name "Hilbert" is also associated with various mathematical concepts and objects named in his honor. These include:
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Hilbert space: A generalization of Euclidean space that extends the methods of vector algebra and calculus from finite-dimensional Euclidean vector spaces to spaces that are possibly infinite-dimensional. Hilbert spaces arise naturally and are important in mathematics and physics, particularly in quantum mechanics.
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Hilbert's paradox of the Grand Hotel: A thought experiment illustrating a counterintuitive property of infinite sets. It posits a hotel with infinitely many rooms, all occupied, and demonstrates that it is possible to accommodate new guests or even infinitely many new guests.
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Hilbert transform: A linear operator that takes a function of one real variable and produces another function of one real variable. It is used in signal processing and other areas.
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Hilbert curve: A continuous space-filling curve.
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Hilbert's axioms: A set of 20 axioms forming the basis for a rigorous treatment of Euclidean geometry.
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Hilbert's basis theorem: States that if a ring R is Noetherian, then the polynomial ring R[x] is also Noetherian.
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Hilbert symbol: A function used in number theory to study quadratic residues.
The legacy of David Hilbert continues to influence mathematical research and education today. His work has had a profound impact on the development of mathematics and its applications.