When1: 1897
When2: 1912
Who: David Hilbert [Hilbert, David]
What: mathematician
Where: Germany
works\ Report on Numbers [1897]; Foundations of Geometry [1899]; 23 Unsolved Problems of Mathematics [1900: at International Congress of Mathematicians, Paris]; Elements and Principles of Mathematics [1912]
Detail: He lived 1862 to 1943 and studied formal systems, proof theory, metamathematics, and Erlanger Program. He studied real numbers using connection, calculation, order, and continuity axioms. He invented Hilbert space and Hilbert-Schmidt theorem. He posed problems {Hilbert program} for 20th century mathematicians to solve [1900]. His tenth problem {Entscheidungsproblem} asked if theorem-proving algorithms are possible. Integral equations and complete orthogonal-system theories relate.
Epistemology
Mathematics can depend on proofs using symbol language {formalism, Hilbert}. Mathematics branches can be formal and studied at higher level {metamathematics, Hilbert}, but do not need infinitely high level. Meaningful mathematics is about finite objects and relations. The infinite hotel {Hilbert hotel} has an infinite number of rooms, so it has infinitely many vacancies, no matter how many people.
Mathematical Sciences>Mathematics>History
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Date Modified: 2022.0224