Archimedes:
The Mathematician With a Hundred Hands

By Gabriel Blanchard

In the modern world as much as antiquity, few minds can hold a candle to Archimedes.

As a man, Archimedes is one of the more obscure figures on our Author Bank. He was born in the city of Syracuse, a Greek colony in Sicily, in 287 BC; he corresponded with friends in Alexandria in Egypt, including Eratosthenes, a mathematician and geographer who was the first person to calculate the circumference of the earth with an error of less than 2%. He died in his home town in 212, in the aftermath of the Roman siege which led to the city’s conquest; according to one version of the story, a soldier commanded him to come and meet Claudius Marcellus, the leader of the campaign, but Archimedes refused because he was in the middle of solving a mathematical problem, and the outraged soldier killed him. (This in turn outraged Marcellus, who had given particular orders that Archimedes not be harmed, possibly in the hope of taking him back to Rome and using his scientific and engineering expertise to benefit the city.) According to a biographer from the time of the Emperor Tiberius, his last act was to place his hands over a diagram he had made in the dust and tell the soldier, “I beg you, do not disturb this.”

The other famous story about him is equally illustrative of his laser-focus upon his work. The ruler of Syracuse had provided a smith with gold to make a crown; however, he suspected the smith had alloyed the crown with silver, which is less precious, and stolen the rest of the gold. Not wanting to melt it down to find out, he asked Archimedes to determine some other way of divining the crown’s real value. One day, when getting into a bath and thus causing the water to rise a little, it struck Archimedes that water is displaced precisely by volume; dividing weight by volume yields density, so he could use the method of water displacement to measure the volume of the crown and use that to determine its density, which would in turn allow him to calculate whether the gold was pure or had been mixed with less-dense silver. According to the story, he was so excited by this realization that he ran out of the house without even stopping to dress, shouting “Heurēka!” or “I’ve found it!”

Give me a place to stand, and I shall move the world.

Archimedes

Whatever the exact historical truth of these stories may be, Archimedes’ contributions to the disciplines of mathematics and engineering are incomparable. One of his ingenious devices was the burning glass, a specially designed mirror that could concentrate sunlight on a distant point; this was used to set fire to enemy ships approaching Syracuse. Another, called Archimedes’ screw, was used on ships in a very different way: by placing a screw-like pillar attached to a hand-crank inside a cylindrical chamber, it was possible by turning the crank to efficiently lift water up through the chamber, thus making it possible to rapidly drain a ship’s hull in case of leaks.

His work on mathematics, particularly geometry, was equally innovative. He is not believed to have discovered the lever, but his famous quotation on it illustrates the principle of the fulcrum, allowing a small force to move disproportionately gigantic masses. He achieved highly accurate approximations of pi and the square root of three, and performed extensive work on calculating the areas of shapes. He was so pleased with his accomplishment in discovering the relationship between the surface area and volume of a sphere and a cylinder that encases it that he had it inscribed on his tombstone, which was discovered by none other than Cicero in the 70s BC.

Curiously enough, Archimedes made only a modest impact on scholarship in his own day, although Claudius Marcellus, the military commander from above, compared him to Briareus, a mythological giant with a hundred hands. It was not until the sixth century after Christ that compilations and commentaries began to be made, by scholars in the Byzantine Empire. Like many ancient authors, he enjoyed a surge of popularity in the Renaissance, and again in the seventeenth century as the science of machines began to advance. Most excitingly, in 1906, two works by Archimedes which were believed lost were rediscovered in a palimpsest (a parchment that has been scraped and over-written with another text) from an Orthodox monastery.

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Every week, we publish a profile of one of the figures from the CLT author bank. For an introduction to classic authors, see our guest post from Keith Nix, founder of the Veritas School in Richmond, VA.

If you liked this piece, check out some of our other posts here at the Journal, like these author profiles of James Madison and John Steinbeck or this essay on the role of poetry in education. And be sure to check out our weekly podcast, Anchored, hosted by our founder Jeremy Tate.

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