Hilbert's problems

Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) at the Paris conference of the International Congress of Mathematicians, speaking on August 8 at the Sorbonne. The complete list of 23 problems was published later, and translated into English in 1902 by Mary Frances Winston Newson in the Bulletin of the American Mathematical Society. Earlier publications (in the original German) appeared in Archiv der Mathematik und Physik.

Of the cleanly formulated Hilbert problems: 3, 6a, 7, 10, 11, 14, 17, 18, 19, and 21 have resolutions that are accepted by consensus of the mathematical community. The status of problems 1, 2, 5, 6b, 8c, 13, and 15 is controversial: there are some results, but there exists some controversy as to whether they resolve the problems. Problems 8a, 8b, 9, 12, 16, 20 and 22 are unresolved or widely agreed as unresolved despite some partial results. Problems 4 and 23 are considered as too vague to ever be described as solved; the withdrawn 24 would also be in this class.