INTRODUCTION

Sitting in a refreshment room at Berlin railway station in 1891, the 29-year-old David Hilbert uttered one of the most memorable lines in the whole history of mathematics. He had been attending the annual meeting of the German Mathematical Society in Halle, and he was waiting with some fellow conference attendees for his connecting train back to Konigsberg. The friends were reflecting on what they believed to have been the most important talk they had heard at the conference. Hermann Wiener had delivered a provocative lecture in which he outlined the need for more rigorous underpinnings to the theory of geometry. Very few people still took Euclid's Elements, written in the third century BCE, as a repository of literal truths, but the primitive elements of geometry had remained largely unchanged since that time (Henderson 2013: 101). “Man mu. jederzeit an Stelle von ‘Punkte, Geraden, Ebenen’ ‘Tische, Stuhle, Bierseidel’ sagen konnen”, Hilbert suddenly interjected into the conversation (Blumenthal 1935: 402–03). This starkly revealing sentence is usually translated into English as: “You can say at any time ‘tables, chairs, beer mugs’ instead of ‘points, straight lines, planes’”.

Such is the retrospective power that has been loaded onto Hilbert's comment that it sounds as though it belongs to an apocryphal story. However, the biographer in question, Otto Blumenthal, was one of Hilbert's closest collaborators. His account was seen by Hilbert before it was despatched for publication, presumably therefore with his blessing. There is still the chance he did not use these exact words and the standard English translation might add a more dramatic gloss to what was actually said. At this stage of his career, though, Hilbert certainly thought it should be possible to substitute any words drawn from a random letter generator for the well-known geometrical concepts of “points”, “lines” and “planes”, yet still leave intact the underlying logical structure through which he would henceforth seek to describe the relationship between points, lines and planes. I know of no contemporary economics imperialist who cites Hilbert's 1891 challenge to the need for confirmed empirical content within mathematical objects as direct inspiration for their activities.