``The first man on the street'' -- tracing a famous Hilbert quote (1900) back to Gergonne (1825) (Q346668)

The starting-point for this paper is a quotation of 1900 from David Hilbert: ``An old French mathematician said: `A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street'.'' This is a comment that appeared in a range of other sources throughout the twentieth century (with or without attribution), and all give rise to the query: who was the French mathematician in question? The authors of this paper identify him as Joseph Diaz Gergonne (1771--1859). In doing so, they add new details to the biographies of both Gergonne and Hilbert, and shed additional light on the dissemination of mathematics in the nineteenth century.