Archimedes of Syracuse was an outstanding ancient Greek mathematician, inventor, physicist, engineer and also an astronomer. Although not much is known about his life, he is considered as one of the most eminent scientists and mathematicians of the classical era.

He established strong foundations in the field of mathematics, physics, particularly in statics, hydrostatics and also explained the principle of the lever. In his lifetime, he made many incredible inventions such as designing innovative machines, including screw pumps, compound pulleys and siege machines.

Archimedes’ father was Phidias, an astronomer. We know nothing else about Phidias other than this one fact and we only know this since Archimedes gives us this information in one of his works, The Sandreckoner. A friend of Archimedes called Heracleides wrote a biography of him but sadly this work is lost.

How our knowledge of Archimedes would be transformed if this lost work were ever found, or even extracts found in the writing of others. There are many stories about how Archimedes made his discoveries. A famous one tells how he uncovered an attempt to cheat King Hieron.

The king ordered a golden crown and gave the crown’s maker the exact amount of gold needed. The maker delivered a crown of the required weight, but Hieron suspected that some silver had been used instead of gold. He asked Archimedes to think about the matter.

One day Archimedes was considering it while he was getting into a bathtub. He noticed that the amount of water overflowing the tub was proportional (related consistently) to the amount of his body that was being immersed (covered by water). This gave him an idea for solving the problem of the crown.

There are several ways Archimedes may have determined the amount of silver in the crown. One likely method relies on an idea that is now called Archimedes’s principle. It states that a body immersed in a fluid is buoyed up (pushed up) by a force that is equal to the weight of fluid that is displaced (pushed out of place) by the body.

Using this method, he would have first taken two equal weights of gold and silver and compared their weights when immersed in water. Next he would have compared the weight of the crown and an equal weight of pure silver in water in the same way. The difference between these two comparisons would indicate that the crown was not pure gold.

Method Concerning Mechanical Theorems describes a process of discovery in mathematics. It is the sole surviving work from antiquity, and one of the few from any period, that deals with this topic.

In it Archimedes recounts how he used a “mechanical” method to arrive at some of his key discoveries, including the area of a parabolic segment and the surface area and volume of a sphere.

The technique consists of dividing each of two figures into an infinite but equal number of infinitesimally thin strips, then “weighing” each corresponding pair of these strips against each other on a notional balance to obtain the ratio of the two original figures. Archimedes emphasizes that, though useful as a heuristic method, this procedure does not constitute a rigorous proof.