Infinite Ascent: A Short History of Mathematics

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, evidence that men and women have used and loved mathematics in the time before time began. Neolithic ax-marks have even suggested that the origins of mathematics lie impossibly far in the past, and that men living in caves, their hairy torsos covered by vile-smelling furs, chipped the names of the numbers onto their ax handles as bison grease spattered over an open fire. And why not? Like language itself, mathematics is an inheritance of the race. The burden of those impossibly distant centuries now disappears. It is roughly six centuries before the birth of Christ. The Greeks are just about to elbow their way into all the corridors of culture. They give every indication of knowing everything and having known it all along. Yet the Babylonians already possessed a remarkably sophisticated body of mathematical knowledge. They were matchless observational astronomers, and they had brought a number of celestial phenomena under the control of precise mathematical techniques. They were immensely clever. "I found a stone, but did not weigh it," one scribe wrote. "I then weighed out six times its weight, added two gin, and then added one third of one seventh, multiplied by twenty-four. I weighed it. [The result came to] one ma-na." "What," the scribe now asks his oil-haired students, "was the original weight of the stone?" Mathematicians are apt to see an all-too-familiar face peeping through the problems of a Babylonian scribetheir face, of course, ubiquitous and always the same. But those classicists sipping sherry in the common room of time had been right all along. The Greeks were there at first light. The natural numbers 1, 2, 3, . . . begin at one and they go on forever, the mathemaBerlinski, David is the author of 'Infinite Ascent: A Short History of Mathematics' with ISBN 9780679642343 and ISBN 067964234X.