Hilbert's twenty-third problem
Encyclopedia
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.
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
. 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
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
. 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.