Archimedes is remembered as a mathematician, philosopher, and inventor. It seems, however, that he did not think as much of his numerous inventions--important and fundamental as they were--as he did of his work in the field of mathematics.

Archimedes was born around 287 B.C. in Syracuse, a town in the Greek colony of Sicily. His father was the astronomer Phidias, and he was related to King Hieron II (308 B.C."-216 B.C.). Archimedes went to Alexandria about 250 B.C. to study under Conon and other mathematicians who were former students of Euclid. He later returned to Syracuse where he apparently stayed for the rest of his life. He was executed by a Roman soldier in 212 B.C.

Archimedes earned the honorary title "father of experimental science" because he not only discussed and explained many basic scientific principles, but he also tested them in a three-step process of...