A Theory Is Not Complete Until You Can Explain It To the Person in the Street

David Hilbert? Mary Winston Newson? Adolphe Quetelet? Joseph Diez Gergonne? Michel Chasles? William Spottiswoode? Henry John Stephen Smith? G. Carey Foster? Alphonse Rebière? Anonymous?

Dear Quote Investigator: In 1900 the influential German mathematician David Hilbert addressed the “International Congress of Mathematicians” held in Paris. He presented a collection of unsolved problems which has had an enormous influence in guiding research during the following century and beyond.

Some of the solutions discovered for these problems have been quite complex and intellectually demanding. Nevertheless, Hilbert indicated in his speech that he placed great value on simplicity and intelligibility. He credited an unnamed old French mathematician with the following remark:

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.

Would you please explore the provenance of this saying?

Quote Investigator: The earliest match known to QI appeared in a letter dated February 25, 1825 from French mathematician Joseph Diez Gergonne to Belgian astronomer and statistician Adolphe Quetelet. Below is an image showing the part of the letter containing the quotation. The spelling in the letter differed a bit from current French spelling: “longtemps” was “longtems” and “raconter” was “racconter”. After the image and French text an English translation is shown. Boldface added to excerpts by QI: 1

Excerpt of Gergonne letter

Il y a longtems que je répète à mes élèves qu’on n’a pas encore le dernier mot de la science sur une théorie, tout aussi longtems qu’on ne l’a pas amenée au point de la racconter à un passant, dans la rue.

For many years I repeated to my students that one does not yet have the last word of science on a theory for as long as one has not brought it to the point of being able to recount it to a passerby on the street.

Below are additional selected citations in chronological order.

Continue reading A Theory Is Not Complete Until You Can Explain It To the Person in the Street

Notes:

  1. 2016 November, Historia Mathematica, Volume 43, Issue 4, “The first man on the street” — tracing a famous Hilbert quote (1900) back to Gergonne (1825) by June Barrow-Green and Reinhard Siegmund-Schultze, (Letter dated February 25, 1825 from Joseph-Diez Gergonne to Adolphe Quetelet; authors of this article obtained a scan of the letter from archivist Olivier Damme), Quote Page 421, Elsevier Inc. (Accessed via sciencedirect.com on September 30, 2021) link