The Great Archimedes

The Greek mathematician and inventor Archimedes, like so many figures from the ancient world, comes down to us not as a fully-fledged human being but as the hero of a handful of exemplary anecdotes. In his brief, accessible book The Great Archimedes, the Italian classicist Mario Geymonat draws on these quasi-legends, showing that they add up to a portrait of Archimedes as the original absent-minded professor. According to Plutarch, for instance, Archimedes was so engrossed in mathematical speculations that "he kept forgetting to eat and to care for his body." Even when his servants dragged him to the bathroom to wash, "he often drew a picture of some geometric figures in the ashes from the heater, and as soon as they had smeared him with oil, he traced some lines on his own limbs with his finger."


There's no way of knowing if this is true, of course, but the magnitude of Archimedes's achievements makes it easy to believe that he never stopped calculating. Geymonat offers brief introductions to his major treatises, some of which survive only in fragments or in Latin or Arabic translation. Archimedes calculated the value of pi to three decimal places, established that the shortest distance between two points is a straight line, and showed how to measure the surface area and volume of a sphere. In a more fanciful work, The Sand Reckoner, he came up with an estimate of how many grains of sand it would take to fill the known universe—his answer was "the number we should represent [in Arabic numerals] by 1 followed by 80,000 million million" zeroes.


But while Archimedes is said to have preferred such abstract theorizing, he was also capable of amazing feats of engineering. Working on a system of levers and pulleys for launching an enormous ship, he is supposed to have declared, "Give me a lever long enough and I will move the world." Most famously, he came up with the principle of displacement while lying in the bath, prompting him to jump out and cry "Eureka, I have found it." It's only a little disillusioning to learn that he applied this epic discovery for the purpose of figuring out whether the ruler of Syracuse had been short-changed, by having his solid-gold crown adulterated with silver.


In the end, Archimedes's unworldliness is said to have cost him his life. In 212 BC, when Syracuse was conquered by the Romans, the victorious general, Claudius Marcellus, "made a public declaration that whoever saved the scientist's life would garner as much glory for saving him as Marcellus himself had for being the conqueror of Syracuse." True to form, even in the chaos of the city's fall, Archimedes was absorbed in sketching geometrical figures in the dirt with a stick. When a Roman soldier came upon him and asked who he was, he was so distracted that—in the words of Valerius Maximus—he "could not say his own name but, protecting the design traced in the dust with his hands, said, 'Please, do not disturb this.' Thus, having given the impression of disregarding the superiority of his conqueror, Archimedes was beheaded, so that he mingled the features of his formula with his blood."


It all sounds a little too symbolic to be true—the man of science destroyed by an ignorant world. As Geymonat says, "the historical Archimedes [has been] tainted by or even blended with mythical characters," so that he seems more like a tutelary spirit of mathematics than a scientist like Isaac Newton. The Great Archimedes reminds us that, as impressive as his legend might be, his actual achievements are more amazing still.




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