Infinite Ascent

Chapter 1

Number

The history of mathematics begins in 532 BC, the date marking the birth of the Greek mathematician Pythagoras. Having fled the island of Samos in order to escape the tyranny of Polycrates, Pythagoras traveled to Egypt, where, like so many impressionable young Greek men, he learned number and measure from Egyptians [and] was astonished at the wisdom of the priests. Thereafter, he settled in southern Italy; he began teaching and quickly attracted disciples. Very little is known directly of his life, except that his contemporaries considered him admirable. Nothing from his own hand remains: He has been preserved against the worm of time by the amber of various literary artifacts. Admission to the Pythagorean sect was evidently based on mathematical ability. Secrecy was enforced and dietary restrictions against beans maintained. New members were required to keep silent for a number of years, a policy that even today many teachers will find admirable, and they were expected during this time to meditate and reflect. Some members of the Pythagorean sect regarded the external world as a prison, a cave filled with flickering shadows and dull brutish shapes. Let me add to this confused but static scene the heat lightning of superb mathematical intuition.

Until the mid-twentieth century, the thesis that in mathematics as in almost everything else, the Greeks were there at first light, did not require an elaborate defense. With their forearms draped in friendship over any number of toga-clad shoulders, classicists who had spent years mastering infernal Greek declensions naturally assumed that the Greeks were fellows of another college. The history of the Ancient Near East has come into sharper focus over the past century, great scholars poring over cuneiform tablets and re-creating the life of ancient empires that had until their work been swallowed up as the impenetrable before. They have found remarkable things, a history before classical history,

David Berlinski received his Ph.D. from Princeton University and has taught mathematics, philosophy, and English at Stanford, Rutgers, the University of Puget Sound, and the Université de Paris at Jussieu. He has been a research fellow at both the International Institute for Applied Systems Analysis in Austria and the Institut des Hautes Études Scientifiques in France. His many books have been translated into more than a dozen European and Asian languages. His essays in Commentary have become famous. A senior fellow at the Discovery Institute in Seattle, he lives and works in Paris.

For mathematically challenged folk like me, David Berlinski comes again to help with a thin volume that, like his A Tour of the Calculus, renders mathematics not easy, but accessible and absorbing. He portrays through history how mathematical thought evolved, from the genius of the few to its application by the many. Personalities, times, cultures, and opportunities all play their dramatic roles and Berlinski, knowing how they interacted, brings them vividly to life. You ll enjoy yourself.
Paul McHugh, Distinguished Service Professor of Psychiatry, Johns Hopkins University

This is literary science at its best. I was charmed by this top-down and introspective presentation of the subject of mathematics. It is not just highly readable; because it is one step above the subject, it can even inspire the professional.
Nassim Nicholas Taleb, Dean s Professor in the Sciences of Uncertainty, University of Massachusetts at Amherst, author of Fooled by Randomness

A humorous and graceful short history of mathematics, quite deceptively easy to read. Berlinski is actually a sophisticated insider, and every page of this book glows with his love of mathematics and with his sardonic appreciation for humanity s foibles.
Gregory Chaitin, IBM Thomas J. Watson Research Center, author of Meta Math! The Quest for Omega