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Archimedes had a wide variety of interests, which included encompassing 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 the tub. 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.

There are three main mechanical inventions credited to Archimedes. 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 way of finding the volume of something by displacement as demonstrated in the story above. Most historians would agree that more important than his great mechanical inventions were his mathematical discoveries.

The mathematical works that have been presented to us by Archimedes could be classified into three groups. The first group consists of works that have as their major objective the proof of theorems relative to the areas and volumes of figures bounded by curved lines and surfaces. The second category contains works that lead to a geometrical analysis of statical and hydrostatical problems and the use of statics in geometry. Miscellaneous mathematical works make up the third group.

Toward the end of Archimedes life, the political situation around him became worse as the years went by. After the death of Hieron II, Syracuse fell into the hands of his grandson, Hieronymus, who changed from the alliance of Rome to the alliance of Carthage. After the Romans heard of this revelation they sent a fleet of ships to capture Syracuse. Archimedes was a key factor to 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 a blaze.

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 preserverence. Archimedes’ theorems, postulates, and inventions are still part of society today. These are some of the reasons that some scolars rank him with the greatest mathematicians in history.