Few certain details remain about the life
of antiquity’s greatest mathematician, Archimedes. We know he was born
in 287 B.C.E. around Syracuse from a report 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 being the author of 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 Archimedes died in 212 B.C.E. at the age of
75 in Syracuse. It is said that he was killed by a Roman soldier, who was
offended by Achimedes, while the Romans seized Syracuse.
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.