Hilbert's sixth problem is to axiomatize those branches of science in which mathematics is prevalent. It occurs on the list of Hilbert's problems given out in 1900. The explicit statement reads 6. Mathematical Treatment of the Axioms of Physics.

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  • Hilbert's sixth problem is to axiomatize those branches of science in which mathematics is prevalent. It occurs on the list of Hilbert's problems given out in 1900. The explicit statement reads 6. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics. In the decade that followed, new foundational physics in the form of quantum theory and special relativity arose. These, clearly, could not have been anticipated when Hilbert formulated the problem. He himself subsequently worked on the axiomatic approach to more classical parts of physics. When it came to formulating general relativity, Hilbert had an influence. The abstract approach of Dirac to the developed quantum mechanics of the 1920s resembles an axiomatic study; but would not be considered to be a complete axiomatisation in mathematical terms. Efforts have been made to put quantum field theory on some axiomatic basis. While the programme suggested by Hilbert has had some influence, therefore, it cannot be said to have been fulfilled along the lines suggested. In fact, fundamental physics still eludes any precise description. Probability theory, however, was put on an axiomatic basis by Kolmogorov in the 1930's, using the machinery of measure theory.
  • O Sexto Problema de Hilbert é um dos mais complicados problemas da famosa lista pois a sua proposta é transformar toda a Física em axiomas e vai de encontro ao fato de que muitas verdades matemáticas algumas vezes não serem correspondidas na física e vice-versa.
  • 希爾伯特第六問題即公理化物理。雖然物理學並非數學，但是兩者之間的關係密切，許多物理學上的概念可藉由數學來明確化，而數學上有一些東西的靈感也是來自於物理學的研究，微積分就是最著名的例子，因此希爾伯特認為能使用數學上公理化的概念來將物理學給公理化，而後來也確實有人進行這項工作，並且也獲得了成功，凡舉古典力學、機率論、熱力學、狹義相對論乃至於量子力學都有人進行公理化的工作。
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  • Hilbert's sixth problem is to axiomatize those branches of science in which mathematics is prevalent. It occurs on the list of Hilbert's problems given out in 1900. The explicit statement reads 6. Mathematical Treatment of the Axioms of Physics.
  • O Sexto Problema de Hilbert é um dos mais complicados problemas da famosa lista pois a sua proposta é transformar toda a Física em axiomas e vai de encontro ao fato de que muitas verdades matemáticas algumas vezes não serem correspondidas na física e vice-versa.
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  • Hilbert's sixth problem
  • Sexto problema de Hilbert
  • 希爾伯特第六問題
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