Shoulders of giants

On an otherwise nondescript day in the year 212 BC, in a city called Syracuse, an invading Roman soldier came upon a 75 year old man. "Follow me to my commander, Marcellus!" the soldier ordered. The old man was closely examining a diagram dotted with circles, oblivious to his surroundings. He refused to go till he had finished solving his problem.

"Do not touch my circles!" he scolded the soldier. That enraged the soldier so much that he drew his sword and killed the old man.

Fortunately, history has forgotten the soldier's name. The man he killed that day was Archimedes.

As far as Rome was concerned, killing Archimedes was a glorious triumph. For the previous three years, Syracuse, then part of the Greek empire, had held off the Roman might with something never seen before: scientific engineering. The Syracusans knew a lot about levers and pulleys and catapults, and they put these instruments to clever use. Grapnels lowered from huge cranes caught the bows of the Roman ships and hoisted them up using pulleys, spilling Rome's proud sailors into the sea. On land, catapulted balls and darts and bolts showered down on Marcellus's men, sending them fleeing in panic.

With techniques like that, Syracuse was showing Rome that brains could beat brawn.

And it was Archimedes who discovered the secrets that enabled Syracuse to build its ingenious machines. It took a three-year siege for Marcellus to finally overcome Syracuse, and for one of his soldiers to kill Archimedes.

One small triumph for Rome, sure. But one giant tragedy for mankind. For Archimedes of Syracuse was a truly brilliant mathematician, physicist and engineer.

He was the first thinker to apply mathematics consistently to physics, so becoming the pioneer of physics as a science. And in searching for general principles to apply to specific engineering problems, he was the first scientific engineer.

And perhaps above all, Archimedes was a champion of method. His results were marvellous in themselves, but he was even more concerned with how he got those results. His method had to be unshakeable. Starting with simple postulates, he used unimpeachable logic to derive his propositions.

The best known of those is Archimedes' Law: an object placed in water displaces an amount of water whose volume equals that of the object. (Well, there's a bit more to it, but that's the gist of it). The king of Syracuse once asked Archimedes to find out whether, as he suspected, his crown was not pure gold. Legend tells us that Archimedes was thinking about the problem while taking a bath one day. He noticed that the water level rose as he sank into the bath. Suddenly realizing the answer, he ran naked through the streets to tell the king of his discovery, shouting "Eureka!" ("I have found it!").

Which may just be the most famous public display of nudity for scientific purposes in history.

Today it is amusing to read of the fiendish machines Archimedes devised to defend Syracuse. They couldn't have been very amusing to the Romans, though. Fed on the virtues of simply overwhelming the enemy with brute force, they were baffled by what happened at Syracuse. Which previous enemy had been as contemptuous of Roman military strength as to lift her ships up and toss her sailors into the sea?

To Archimedes, though, the machines were mere applications of his principles: the lever, the pulley and others. And just as significant to him as the victories of his machines were his other applications of those principles.

For example, he used the principle of the lever to derive the volume of a sphere. His elegant method considered how differing circles balanced each other on an imaginary lever, so deducing their weights and volumes. He went on to use the same method to find the volume of other objects of mathematical interest, like the ellipsoid. In fact, Archimedes was so fond of this method that, at his request, his tombstone was engraved with a sphere in a cylinder, illustrating his method.

Like other thinkers of his time, Archimedes also gave a lot of thought to calculating pi, the ratio of the circumference of a circle to its diameter. Now this was an interesting pursuit because, of course, pi cannot be expressed as a fraction, a ratio between two numbers -- so it is impossible to state an exact value for it. It startled the Greeks that as simple an object as a circle contained within it the diabolical irrationality of pi.

Archimedes, characteristically less concerned with the value than with how to find it, was the first to find a method to calculate pi to any desired degree of accuracy. Not just that, it was 19 centuries before his method was bettered. In this, as in his other pursuits, Archimedes stood head and shoulders above his contemporaries. And above most who came afterward as well.

So if an ignorant Roman killed the man in 212 BC, his ideas and his influence on mathematics live on. Not even the might of a great Empire could kill those.

For you might say, it was Archimedes who first showed the world that the thinkers could defeat the thugs.