American Scientist

To the Editors:

Daniel Silver’s interesting—and important—article, “The New Language of Mathematics” (November–December), deserves to be read widely (at least as widely as Felix Mendelssohn’s Lieder ohne Worte is listened to!).

Josiah Willard Gibbs’s rare but “forceful” declaration to his fellow faculty members, “Gentlemen, mathematics is a language,” is well-known to economists, at least those of my vintage, because it (minus “Gentlemen”) was the epigraph of the pioneering book, Foundations of Economic Analysis by Paul Samuelson. Five years later, on reflection, Samuelson felt that the indefinite article a in the Gibbs quote was superfluous!

I particularly enjoyed Silver’s anecdote on Maria Agnesi and the wonderful diagram of Guido Grandi’s adaptation of versiera—and the professor at Cambridge mistranslating the word as l’avversiera!

Silver fails, however, to harness on his side one of the great philosophers of the 20th century and an equally great and idiosyncratic mathematician of the same century: Ludwig Wittgenstein and Luitzen Brouwer.

They wanted to develop a philosophy and a mathematics, respectively, free of the mysticism—Wittgenstein referred to it as the “bewitchment”—of language, when used (indiscriminately) in the formalization of mathematics (and also, in the case of Brouwer, logic; in the case of Wittgenstein the logic part was by way of rejecting the approach in his work Tractatus Logico-Philosophicus).

Legend has it that Wittgenstein returned to philosophy after hearing Brouwer’s lecture, “Mathematics, Science and Language” in March 1928 in Vienna.

K. Vela Velupillai
Solna, Sweden

Dr. Silver responds:

I thank Dr. Velupillai also for mentioning Wittengstein and Brouwer. I notice that Dr. Velupillai is writing from Sweden. It was the librarian at the Institut Mittag-Leffler, Djursholm, who told me the full story about the “witch of Agnesi” and directed me to the relevant historical documents. (The institute has an astonishing library of rare mathematics books!) I am always impressed by the erudition of American Scientist readers.