At the International Congress of Mathematics in the year 1900 in Paris, David Hilbert gave a talk in which he stated 23 open problems that he regarded central for the development of mathematics. These became famous as Hilbert’s 23 problems and have indeed considerably influenced mathematics in the 20th century.

David Hilbert, Mathematical Problems, Bulletin of the American Mathematical Society, vol. 8, no. 10 (1902), pp. 437-479. Earlier publications (in the original German) appeared in Göttinger Nachrichten, 1900, pp. 253-297, and Archiv der Mathematik und Physik, 3dser., vol. 1 (1901), pp. 44-63, 213-237. (AMS, pdf, html)

Felix E. Browder. Mathematical Developments Arising from Hilbert Problems. Proceedings of Symposia in Pure Mathematics. XXVIII.2. American Mathematical Society.