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- Hilbert's_program abstract "In mathematics, Hilbert's program, formulated by German mathematician David Hilbert, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic.Gödel's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics. In his first theorem, Gödel showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete: it is possible to construct a statement that can be shown to be true, but that cannot be derived from the formal rules of the system. In his second theorem, he showed that such a system could not prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger with certainty. This refuted Hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore anything else.".
- Hilbert's_program wikiPageExternalLink 0508572.
- Hilbert's_program wikiPageExternalLink hilbert-program.
- Hilbert's_program wikiPageExternalLink hilbert.html.
- Hilbert's_program wikiPageID "607286".
- Hilbert's_program wikiPageRevisionID "588913484".
- Hilbert's_program hasPhotoCollection Hilbert's_program.
- Hilbert's_program subject Category:Hilbert's_problems.
- Hilbert's_program subject Category:Mathematical_logic.
- Hilbert's_program subject Category:Proof_theory.
- Hilbert's_program type Abstraction100002137.
- Hilbert's_program type Attribute100024264.
- Hilbert's_program type Condition113920835.
- Hilbert's_program type Difficulty114408086.
- Hilbert's_program type Hilbert'sProblems.
- Hilbert's_program type Problem114410605.
- Hilbert's_program type State100024720.
- Hilbert's_program comment "In mathematics, Hilbert's program, formulated by German mathematician David Hilbert, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent.".
- Hilbert's_program label "Hilbert's program".
- Hilbert's_program label "Hilbertprogramm".
- Hilbert's_program label "Programa de Hilbert".
- Hilbert's_program label "Programa de Hilbert".
- Hilbert's_program label "Programma di Hilbert".
- Hilbert's_program label "Programma van Hilbert".
- Hilbert's_program label "Programme de Hilbert".
- Hilbert's_program label "برنامج هيلبرت".
- Hilbert's_program label "ヒルベルト・プログラム".
- Hilbert's_program label "希尔伯特计划".
- Hilbert's_program sameAs Hilbertův_program.
- Hilbert's_program sameAs Hilbertprogramm.
- Hilbert's_program sameAs Programa_de_Hilbert.
- Hilbert's_program sameAs Programme_de_Hilbert.
- Hilbert's_program sameAs Program_Hilbert.
- Hilbert's_program sameAs Programma_di_Hilbert.
- Hilbert's_program sameAs ヒルベルト・プログラム.
- Hilbert's_program sameAs Programma_van_Hilbert.
- Hilbert's_program sameAs Programa_de_Hilbert.
- Hilbert's_program sameAs m.02vz8z.
- Hilbert's_program sameAs Q968548.
- Hilbert's_program sameAs Q968548.
- Hilbert's_program sameAs Hilbert's_program.
- Hilbert's_program wasDerivedFrom Hilbert's_program?oldid=588913484.
- Hilbert's_program isPrimaryTopicOf Hilbert's_program.