Hilbert's twenty-third problem

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Hilbert's twenty-third problem is the last of Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. In contrast with Hilbert's other 22 problems, his 23rd is not so much a specific "problem" as an encouragement towards further development of the calculus of variations. His statement of the problem is a summary of the state-of-the-art (in 1900) of the theory of calculus of variations, with some introductory comments decrying the lack of work that had been done of the theory in the mid to late 19th century.