David Hilbert Problems

 

By Unknown author - Possibly Reid, Constance (1970) Hilbert, Berlin, Heidelberg: Springer Berlin Heidelberg Imprint Springer, p. 230 ISBN: 978-3-662-27132-2., Public Domain, https://commons.wikimedia.org/w/index.php?curid=36302

In 1900, a renowned German mathematician, David Hilbert, published 23 problems for the mathematical community to work on for the 20th century. At the time of the publication, the problems had not been solved. A link to the English translation of the problems: S0002-9904-1902-00923-3.pdf (ams.org)

To date, 8 of the problems have been resolved, meaning the problem was solved or a proposed proposition was proven or disproven. Another 9 have been partially resolved, meaning there exists some controversy as to whether the proposed solution fully resolves the question. Six problems remain unsolved.

A breakdown of the problems' status is given here: Hilbert's problems - Wikipedia.

Problem 2 was written about in a prior post about Kurt Gödel's incompleteness theorem.

Problem 18 sought a proof for the densest sphere packing which wasn't resolved until 1998. Also see this blog's post on sphere packing in higher dimensions.

The Simons Foundation’s Mathematics and Physical Sciences (MPS) division recently published: Solved, Unsolved and Unsolvable: The Status of Hilbert’s 23 Problems in Mathematics