Archimedes was one of antiquity’s greatest mathematicians. Few certain details remain about his life. We know he was born in 287 BCE in Syracuse, based on a report from about 1400 years after the fact.
Archimedes tells about his father, Pheidias, in his book The Sandreckoner. Pheidias was an astronomer who was famous for authoring a treatise on the diameters of the sun and the moon. Historians speculate that Pheidias’ profession explains why Archimedes chose his career. Some scholars have characterized Archimedes as an aristocrat who actively participated in the Syracusan court and may have been related to the ruler of Syracuse, King Hieron II. We also know that Archimedes died in 212 B.C.
Archimedes died at the age of 75 in Syracuse. It is said that he was killed by a Roman soldier who was offended by him while the Romans seized Syracuse. Archimedes had a wide variety of interests, including statics, hydrostatics, optics, astronomy, engineering, geometry, and arithmetic.
Archimedes had more stories passed down through history about his clever inventions than his mathematical theorems. This is believed to be so because the average mind of that period would have no interest in the Archimedean spiral, but would pay attention to an invention that could move the earth. Archimedes’ most famous story is attributed to a Roman architect under Emperor Augustus named Vitruvius. Vitruvius asked Archimedes to devise some way to test the weight of a gold wreath.
Archimedes was unsuccessful until one day, as he entered a full bath, he noticed that the deeper he submerged into the tub, the more water flowed out of it. This made him realize that the amount of water that flowed out of the tub was equal to the volume of the object being submerged. Therefore, by putting the wreath into the water, he could tell by the rise in water level the volume of the wreath, despite its irregular shape. This discovery marked the Law of Hydrostatics, which states that a body immersed in fluid loses weight equal to the weight of the amount of fluid it displaces. Archimedes is credited with three main mechanical inventions. The first one is the Archimedean screw, which supposedly could serve as a water pump.
The second invention was the compound pulley. The third invention was the method of finding the volume of an object by displacement, as demonstrated in the story above. Most historians agree that Archimedes’ mathematical discoveries were more important than his great mechanical inventions. Archimedes’ mathematical works can be classified into three groups. The first group consists of works that aim to prove theorems related to the areas and volumes of figures bounded by curved lines and surfaces. The second category contains works that analyze statical and hydrostatical problems geometrically and use statics in geometry.
Miscellaneous mathematical works make up the third group. Toward the end of Archimedes’ life, the political situation around him worsened. After the death of Hieron II, Syracuse fell into the hands of his grandson, Hieronymus, who switched from the alliance of Rome to the alliance of Carthage. The Romans sent a fleet of ships to capture Syracuse upon hearing of this revelation. Archimedes was a key factor in the Syracusians’ ability to hold off the Romans for so long.
He is said to have created catapults to hurl rocks and used compound pulleys with giant hooks to rip the Roman ships apart. The most well-known invention to ward off the Romans was the construction of a series of giant lenses used to magnify the sun’s rays and set Roman ships ablaze. The theorems that Archimedes discovered and worked on raised Greek mathematics to a whole new level. He undertook difficult problems in both mechanics and mathematics with great perseverance. Archimedes’ theorems, postulates, and inventions are still part of society today. These are some of the reasons that some scholars rank him with the greatest mathematicians in history.
