Editing Hilbert's problems (section)

{{Short description|23 mathematical problems stated in 1900}}
{{CS1 config|mode=cs1}}
[[File:Hilbert.jpg|thumb|David Hilbert]]
'''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&nbsp;8 at the [[University of Paris|Sorbonne]]. The complete list of 23&nbsp;problems was published later, in English translation in 1902 by [[Mary Frances Winston Newson]] in the ''[[Bulletin of the American Mathematical Society]]''.<ref name="Hilbert_1902">{{cite journal |last=Hilbert |first=David |title=Mathematical Problems |url=https://www.ams.org/journals/bull/1902-08-10/home.html |journal=[[Bulletin of the American Mathematical Society]] |volume=8 |issue=10 |year=1902 |pages=437–479|doi=10.1090/S0002-9904-1902-00923-3 |doi-access=free }}
</ref> Earlier publications (in the original German) appeared in ''Archiv der Mathematik und Physik''.<ref name="Hilbert_1901">{{cite journal |last=Hilbert |first=David |title=Mathematische Probleme | url=https://www.digizeitschriften.de/id/252457811_1900%7Clog37?tify=%7B%22pages%22%3A%5B269%5D%2C%22pan%22%3A%7B%22x%22%3A0.427%2C%22y%22%3A0.819%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.525%7D#navi |journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse (News of the Society of Sciences at Göttingen, Mathematical-Physical Class) |year=1900 |pages=253–297 |lang=de}} and {{cite journal |last=Hilbert |first=David |title=Mathematische Probleme |journal=Archiv der Mathematik und Physik |series=3rd series |volume=1 |year=1901 |pages=44–63, 213–237 |url=https://babel.hathitrust.org/cgi/pt?id=mdp.39015049309860&seq=62 |lang=de}}</ref>

Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, 21, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6,{{refn|group=lower-alpha|Number&nbsp;6 is now considered a problem in physics rather than in mathematics.}} 9, 11, 12, 15, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the [[Riemann hypothesis]]), 13 and 16{{refn|group=lower-alpha|Some authors consider this problem as too vague to ever be described as solved, although there is still active research on it.}} unresolved. Problems 4 and 23 are considered as too vague to ever be described as solved; the withdrawn 24 would also be in this class.