In Königsberg on 8 September 1930, David Hilbert addressed the yearly meeting of the Society of German Natural Scientists and Physicians (Gesellschaft der Deutschen Naturforscher und Ärzte). Generally regarded as the world’s leading mathematician, Hilbert was born and educated in Königsberg and spent the early years of his career there. Retiring at age sixty-eight from his professorship at Göttingen, he was being honored by his home city. Hilbert forcefully delineated a basic tenet of his research philosophy—that every mathematical problem is solvable—and countered a widespread but controversial opposing opinion. Shortly afterward, he read on German radio a four-minute version of the finale of his speech. This excerpt stands on its own as a dramatic poem or anthem that has inspired many mathematicians and will continue to do so, and it has the potential to reinforce public appreciation of the historical and present context of mathematical research.
On subsequent pages, you will have the opportunity to listen to Hilbert's radio address (Hilbert  1971) while reading a German transcription, an English translation, or a side-by-side transcription and translation.
Hilbert’s address did not spring forward in isolation. It climaxed a development that is evidenced in his earlier work, and reacted to broad and deep trends in philosophy and mathematical culture. The present article concludes with a discussion that will steer the reader to some of this lore. It identifies persons and explains terms that Hilbert mentioned, and provides both background for the occasion and a hint of subsequent related developments.