De Siegel a Mordell

Göttingen, March 3, 1964.

Dear Professor Mordell,

Thank you for the copy of your review of Lang's book. When I first saw this book, about a year ago, I was disgusted with the way in which my own contributions to the subject had been disfigured and made unintelligible. My feeling is very well expressed when you mention Rip van Winkle!

The whole style of the author contradicts the sense for simplicity and honesty which we admire in the works of the masters in number theory—Lagrange, Gauss or, on a smaller scale, Hardy, Landau. Just now Lang has published another book on algebraic numbers which, in my opinion, is still worse than the former one. I see a pig broken into a beautiful garden and rooting up all flowers and trees.

Unfortunately there are many "fellow-travelers" who have already disgraced a large part of algebra and function theory; however, until now, number theory had not been touched. These people remind me of the impudent behaviour of the national socialists who sang: "Wir werden weiter marschieren, bis alles in Scherben zerfällt!"

I am afraid that mathematics will perish before the end of this century if the present trend for senseless abstraction—I call it: Theory of the empty set—cannot be blocked up. Let us hope that your review may be helpful.

I still remember the nice time we had together during your visit in Göttingen.

With best wishes, also to Mrs. Mordell,

Carl Siegel.

[De acuerdo con lo que se puede leer en la cuenta de David C. Kandathil en Google+, el original de esta carta se encuentra en la biblioteca del College of St. John de la Universidad de Cambridge.]

Apuntes para una historia del problema de los NPI

«... In 1985, a high school senior in Hawaii named David Williamson, who was taking mathematics courses at the University of Honolulu, proved that if an odd perfect number exists, it must have exactly one prime factor that, when divided by 4, leaves a remainder of 1. Williamson's professor didn't know whether the result was original and suggested he write to the legendary Erdös, who had just come through town. Williamson eventually got a letter back from Erdös: 'The result you proved is in fact due to Euler. He also proved that every even perfect number is of the form 2^p-1(2^p-1) where 2^p-1 is a prime. It is also known (proved by Carl Pomerance) that an odd perfect number if it exists must have at least 7 distinct prime factors. Perhaps the following problem of mine will interest you...' Williamson, now a combinatorialist at IBM, was thrilled. 'This letter to a high school student won't rank very high on Erdös's list of accomplishments, but it did mean a lot to me.'»

Paul Hoffman, The man who loved only numbers: the story of Paul Erdös and the search for mathematical truth. Hyperion, NY, 1998, pp. 47-48.