Wednesday, December 10, 2008
Wednesday Math, Vol. 51: The wonder of the ancient world
Conventional wisdom now has it that the greatest mathematician of the ancient world was Archimedes of Syracuse, subject of this bronze statue found in Berlin. Why Archimedes is given this honor over other famous names from the time before Christ like Euclid and Pythagoras is a matter of modern sensibilities. The historical data on Euclid and Pythagoras is very sketchy, and it is hard to say how much of what they are credited with was actually their work or the work of students who honored their master by putting his name on their best work as well as that which the teacher actually produced. In comparison, we have a lot of historical information on Archimedes, including the story of his death recounted in a biography of a Roman general.
Archimedes had no students and left behind no school. He was related to the royalty of his Sicilian city, and made a comfortable living by creating remarkable inventions, only a few of which survive to this day. This focus on the practical side makes Archimedes much more like a modern mathematician like Newton, Gauss, Euler and even Von Neumann in the 20th Century, who were also physicists and inventors. In fact, Archimedes' name was renowned for many centuries only as an inventor, and the first surviving commentaries on his mathematics were not published until the fifth century of the Christian era.
Let me tell an abbreviated biography of Archimedes based on his three most famous surviving quotes.
Eureka! There are only a few stories in history that involve great men running naked through the streets, and this is one of them. (St. Francis stood naked before a crowd, but there is no mention of him running.) Archimedes while in the bathtub figures out the displacement properties of fluids, and realizing this is the solution to a problem the king had tasked him to solve, he runs through the streets of Syracuse naked, shouting "I have found it!" (I always imagine some guy seeing him saying "Well, it's not that hard to find, Archimedes. You probably find it when you wake up every morning and have to pee.")
Give me a lever and a place to stand and I could move the earth. Archimedes made a demonstration at the palace of moving a huge boulder that the strongest man could not budge on his own. Archimedes of course cheated, which is to say he used his brain, which gave him an unfair advantage over the rest of humanity. He used a lever and fulcrum. He was very clever with what were called "the simple machines" when I was in grade school. The Archimedes Screw, one of his few inventions that survive today, is a way to pump water uphill, using something like a corkscrew fitted snugly inside a cylinder. The design is still used in irrigation systems around the world to this day.
Don't disturb my circles! Many of Archimedes' most remarkable inventions do not survive to this day, because they were secret weapons. In the biography of the Roman general Marcellus, the death of Archimedes is told as part of the story of the conquest of Syracuse, which was no small task. Archimedes' weapons made it very difficult to attack Syracuse. Among the designs that we have been able to piece together from contemporary descriptions is a water mine powered by animals turning a large wheel on the shore connected by pulleys to underwater spikes on a screw. It is said that large boats could be lifted out of the water and shaken apart violently. Marcellus wanted the great man's secrets for himself and he gave the order that Archimedes was not to be harmed.
So there's a huge battle going on, and Archimedes, now well into his seventies, is home working on a geometry problem. Because paper was so expensive, any "scratch" work done by mathematicians then was done very large on a smooth courtyard covered with a thin layer of sand. A soldier bursts into Archimedes' home, and whether because he was deaf from advanced age or just lost in thought like mathematicians often are, he first notices the soldier when the young man's shadow blocks the work he is doing. "Don't disturb my circles!" the old man barks at the soldier, who takes offense at the disrespect for the authority his sword gave him, and stabs Archimedes through the belly. Marcellus is very upset that the genius inventor is gone, but he decides to honor Archimedes by building the great man a tomb, topped with a likeness of the work that Archimedes considered to be his greatest mathematical discovery.
Next week: Archimedes' tomb.