Editing Hilbert's second problem (section)

{{Short description|Consistency of the axioms of arithmetic}}
In [[mathematics]], '''Hilbert's second problem''' was posed by [[David Hilbert]] in 1900 as one of his [[Hilbert's problems|23 problems]].  It asks for a proof that arithmetic is [[consistency proof|consistent]] &ndash; free of any internal contradictions. Hilbert  stated that the axioms he considered for arithmetic were the ones given in {{harvtxt|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.