Archimedes

archimedes biography ancient greek mathematician inventor eureka principle mathematics physics

Introduction: the Greatest Mind of Antiquity

Archimedes of Syracuse stands at the very summit of ancient intellectual achievement. Mathematician, physicist, engineer, astronomer, and inventor, he compressed into a single lifetime a volume of original discovery that would not be equalled for nearly two thousand years. He calculated the value of pi to a precision that remained unsurpassed in the Western world for centuries. He determined the surface area and volume of a sphere using a method that prefigured integral calculus. He formulated the first rigorous statement of the principle of the lever, demonstrated why floating bodies behave as they do, and used that knowledge to expose a fraud upon a king. He designed war machines of such terrifying ingenuity that they held the entire Roman army at bay for three years. He wrote letters to the finest mathematicians of the ancient world, sharing not only his conclusions but the mechanical intuitions that led him to them, creating in the process a document that would be lost for a millennium, rediscovered on a parchment scraped clean by a medieval monk, and ultimately recognized as the closest thing antiquity produced to a treatise on the foundations of calculus.

To understand Archimedes is to understand something profound about the nature of genius. He was not the product of a long institutional tradition, working carefully within an established framework. He was a man who repeatedly outpaced every tradition he inherited, who reached results that his contemporaries could verify but not replicate, and who left behind works so far ahead of their time that the mathematicians of the Renaissance struggled to absorb them sixteen centuries after his death. The philosopher Alfred North Whitehead observed that the history of Western mathematics might have been very different had Archimedes been succeeded by even one mathematician of comparable power. That he was not, and that his methods lay largely dormant until Newton and Leibniz independently rediscovered the ideas of the calculus in the seventeenth century, is one of the great tragedies of intellectual history.

This biography traces the full arc of Archimedes' life and work: the political and cultural world of Syracuse in which he was born and died; his early formation and his years studying in Alexandria, the intellectual capital of the Hellenistic world; his relationship with King Hiero II, the enlightened monarch who gave him the resources and the commissions that shaped much of his practical work; his extraordinary series of mathematical treatises, each a complete and self-contained masterpiece; his practical inventions, from the celebrated hydraulic screw to the terrible engines of war that prolonged Syracuse's independence; his formulation of the physical principle that bears his name; the circumstances of his violent death when the Romans finally breached the walls of Syracuse; and the long, complicated story by which his writings were preserved, lost, partially recovered, and ultimately restored to the world through the most dramatic manuscript discovery of the twentieth century.

Archimedes lived at the intersection of two worlds: the serene, timeless world of pure mathematical contemplation, and the violent, contingent world of Mediterranean geopolitics in the third century before the common era. He served both with equal distinction, and the tension between them ultimately defined both his life and his death. To read his surviving works today is to encounter a mind of almost preternatural clarity, moving through problems of extraordinary difficulty with a confidence and economy that can still, after more than two thousand years, produce a sensation that the ancient Greeks called thaumazein, the astonishment that is the beginning of all philosophy.

The World of Ancient Syracuse