The Crisis of Principles in Greek Mathematics (MP3 download)
By Pat Corvini
"By the end of the Golden Age of Greece, mathematics had become man's most highly developed science; but recent developments had undermined confidence in the validity of its foundations. Greek mathematics stagnated until two inventions by the brilliant Eudoxus (a new theory of proportions, and the method of exhaustion) resolved the foundations crisis and enabled further progress, culminating in the work of Archimedes."
That's the traditional interpretation. In this fast-paced and exciting course, Dr. Corvini challenges this view and argues that it rests on a crucial misunderstanding of the science of mathematics. In terms accessible to anyone, she explains how Eudoxus's proofs in fact left the earlier conceptual questions unresolved, setting up a theory-practice dichotomy that persists to the present day—and demonstrates that the actual history supports a proper view of mathematics as an inductive science.
This course was recorded at the 2004 Objectivist Summer Conference in Wintergreen, VA.
(MP3 download; 5 hrs., 13 min., with Q & A, 230.09 MB)