The Impact of Modern Mathematics on Ancient Mathematics

Abstract

Edith Prentice Mendez found this lecture among Wilbur Knorr’s papers after his death in March, 1997. Although Knorr probably never intended to publish it — and he surely would have attended to its occasional roughness — Ken Saito and I consider it an important methodological reflection on his just completed work on the early proportion theory,¹ but with much general interest. The three main examples he | discusses, the theory of irrationals, the alleged foundations crisis in the fifth century and the problem of constructibility, remain important morality tales for contemporary researchers. Among specialists, the pendulum may have swung largely in the other direction, and for that reason, it is useful to quote a letter which warns against the opposed impediment to historical understanding. I thank Joseph Dauben for drawing it to my attention by sending me his transcription of it.