It must be remembered, though, that Hilbert was a figure of towering stature in early twentieth-century mathematics; and also that he lived and worked in the atmosphere of German academia, where university professors were looked up to by their students and subordinates as remote and omniscient gods, to be approached only with the utmost deference. Not only was a professor not ever to be addressed as anything less elevated than “Herr Professor,” even his wife became “Frau Professor.” For the very grandest of these Olympians, indeed, even “Herr Professor” was inadequate. The most exceptional individuals were awarded the title “Geheimrat” by the German government—a rank roughly equivalent to a British knighthood. The correct form of address was then “Herr Geheimrat,” though Hilbert himself did not care for this level of formality.

Given all of this, it is not surprising that if by good fortune you got sufficiently close to one of these deities to hear him speak, you would not soon forget his words. It is also the case, to be sure, that such giants caused a certain amount of unverifiable apocrypha to be generated about them. Still, I think the balance of the evidence, circumstantial though it be, leads one to believe that Hilbert did, indeed, at some point utter the Hilbert-Pólya Conjecture, or something equivalent to it. (To simply say “the Pólya Conjecture” would be confusing, by the way, as there is another, different conjecture known by that name.)