You Are More Likely to Be Remembered by Your Expository Work

Let us look at two examples, beginning with Hilbert. When we think of Hilbert, we think of a few of his great theorems, like his basis theorem. But Hilbert’s name is more often remembered for his work in number theory, his Zahlbericht, his book Foundations of Geometry, and for his text on integral equations. The term “Hilbert space” was introduced by Stone and von Neumann in recognition of Hilbert’s textbook on integral equations, in which the word “spectrum” was first defined at least twenty years before the discovery of quantum mechanics. Hilbert’s textbook on integral equations is in large part expository, leaning on the work of Hellinger and several other mathematicians whose names are now forgotten.

Similarly, Hilbert’s Foundations of Geometry, the book that made Hilbert’s name a household word among mathematicians, contains little original work and reaps the harvest of the work of several geometers, such as Kohn, Schur (not the Schur you have heard of), Wiener (another Wiener), Pasch, Pieri, and several other Italians.

Again, Hilbert’s Zahlbericht, a fundamental contribution that revolutionized the field of number theory, was originally a survey that Hilbert was commissioned to write for publication in the Bulletin of the German Mathematical Society.

— Ten Lessons I Wish I Had Been Taught

— Gian-Carlo Rota

2012.05.11 Friday ACHK