David Hilbert

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David Hilbert (1862-1943) was a German mathematician known for several contributions:

  • Solving several important problems in the theory of invariants. Hilberts basis theorem solved the principal problem in the 1800s invariant theory by showing that any form of a given number of variables and of a given degree has a finite, yet complete system of independent rational integral invariants and covariants.
  • Unifying the field of algebraic number theory with his 1897 treatise Zahlbericht (literally "report on numbers").
  • Providing the first correct and complete axiomatization of geometry with his 1899 book Grundlagen der Geometrie ("Foundations of Geometry").
  • His suggestion in 1920 that mathematics be formulated on a solid logical foundation (by showing that all of mathematics follows from a system of axioms, and that that axiom system is consistent). Unfortunately, Gödel's Incompleteness Theorem showed that his grand plan was impossible.
  • Hilberts paradox, (also called the infinite hotel paradox), a musing about strange properties of the infinite.

Hilbert's 23 problems are:

Currently problems 1, 2, 3, 5, 10, 14, 21 are solved and 7, 8, 9 are not.(what about problems 4,6,11,12,13,15,16,17,18,19,20,21,22,23 ? PME link doesn't say anything about them or is vague)

Further information: