Hilbert's second problem
One of twenty-three, asking to prove the consistency of arithmetic axioms
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions.
Nº Q13424667 ★
Common · Knowledge
Hilbert's second problem
One of twenty-three, asking to prove the consistency of arithmetic axioms
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions.
From Wikipedia
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions. Hilbert stated that the axioms he considered for arithmetic were the ones given in Hilbert (1900), which include a second order completeness axiom. In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new light on the problem. Some feel that Gödel's theorems give a negative solution to the problem, while others consider Gentzen's proof as a partial positive solution.
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