Archimedes | 10 Facts On The Ancient Greek Mathematician


Archimedes was an ancient Greek mathematician, scientist and inventor. Little is known about the personal life of Archimedes and what is known comes from the histories authored by Plutarch, Cicero and other historians several centuries after his death. Though he is now considered one of the greatest mathematicians of all time, much of Archimedes’ fame during his time came from the inventive war machines he built to aid his native city Syracuse. There are many legends associated with him, the most famous of which is the “Eureka” story. He is also credited with many famous quotations including his moving the earth quote and the last words he said before being killed by a Roman soldier. Know about the life, education, career and death; as well as legends and quotations of Archimedes through these 10 interesting facts.


#1 He was probably related to the King of Syracuse

Archimedes was born around 287 BC in the seaport city of Syracuse in Sicily. Syracuse was one of the major powers in ancient Greece and has been described as “the greatest Greek city and the most beautiful of them all”. Its ruler at the time was King Hiero II. Little is known about the family of Archimedes. He was the son of Phidias, an astronomer. We know this as Archimedes gives us this information in one of his works, The Sandreckoner. According to Plutarch, the ancient Greek biographer and essayist, Archimedes was related to King Hiero II. Historians believe that he at least had a friendship with the king of Syracuse even if he wasn’t related to him. It is not known whether Archimedes married or had children.

Coin of King Hiero II of Syracuse
Coin of King Hiero II of Syracuse, possible relative of Archimedes


#2 He most likely studied in Alexandria

The city of Alexandria in Egypt was the intellectual and cultural center of ancient Greece at the time of Archimedes. Though Archimedes born, died and lived most of his life in Syracuse, it is highly likely that as a young man he studied in Alexandria with the successors of another great Greek mathematician Euclid. This can be deduced from the fact that he personally knew other mathematicians who were working there like Conon of Samos and Eratosthenes of Cyrene; and he sent his results to Alexandria with personal messages. Also, Archimedes was familiar with the mathematics which had developed in Alexandria.

Archimedes 1620 Portrait
1620 Portrait of Archimedes by Domenico Fetti


#3 Archimedes allegedly ran naked through the streets yelling “Eureka”

The most famous story related to Archimedes involves a challenge presented to him by King Hiero II. The king had supplied pure gold to a goldsmith to make a crown for a temple but he was uncertain about the finished product doubting whether the goldsmith had mixed some silver in the crown. He gave Archimedes the task to find the purity of the crown without damaging it. After being troubled for a while, Archimedes, supposedly in his bath, discovered that there was a direct correlation of the water overflowing from the tub with his immersed body. He then allegedly ran through the streets naked yelling, “Eureka” (“I have found [it]!”). Eureka has since become a common interjection to celebrate a discovery or invention. The test was conducted and it was ultimately proved that silver had indeed been mixed in the crown. Whether or not the alleged incident took place, Archimedes did formulate the famous Archimedes principle which could be used to solve the problem he had been presented.

Archimedes' Eureka moment
16th-century illustration of Archimedes’ Eureka moment


#4 He famously said that he could topple the earth if given an apt place to stand on

A lever is a machine consisting of a rigid rod pivoted at a fixed hinge, or fulcrum. In his book On the Equilibrium of Planes, Archimedes proved the law of the lever using geometric reasoning. It shows that if the distance a from the fulcrum to where the input force is applied (point A) is greater than the distance b from the fulcrum to where the output force is applied (point B), then the lever amplifies the input force. Archimedes understanding of his principle of mechanical advantage caused him to remark, ‘Give me a place to stand, and I shall move the Earth with it’. Hypothetically speaking, the distance required to do this might be exemplified in astronomical terms as the approximate distance to the Circinus galaxy, about 9 million light years away.

Archimedes moving the earth
A cartoon of Archimedes moving the earth with the aid of a lever


#5 The Archimedes’ principle is his most famous accomplishment

The Archimedes’ principle is a law in hydrostatics formulated by Archimedes which states that a body totally or partially immersed in a fluid is subject to an upward force (buoyant force) that is equal in magnitude to the weight of fluid it displaces. Thus, the net upward force on the object is the difference between the buoyant force and its weight. If this net force is positive, the object rises; if negative, the object sinks; and if zero, the object remains in place without either rising or sinking. Archimedes’ principle is a law of physics fundamental to fluid mechanics and it has numerous applications including the hydrometer, which uses it to determine the specific gravity (relative density) of liquids; designing of ships and submarines; and in controlling the flight of a hot-air balloon.

Archimedes' Principle diagram
Diagramatic representation of Archimedes’ Principle


#6 Archimedes is considered one of the greatest mathematicians of all time

Archimedes is regarded as the greatest mathematician of antiquity and his achievements in the field are numerous and path breaking. He invented and developed methods similar to calculus and used them to find, among other things, the area of a circle; the surface area and volume of a sphere; the area under a parabola; and an accurate estimation of the value of pi, considered one of his most important achievements. He also invented a system for expressing large numbers. Apart from his accomplishments in mathematics, Archimedes laid the foundation of hydrostatics through his work On Floating Bodies, the first known work in the field. However, he was more famous in his life for his inventions than his other contributions.


#7 He was most renowned in ancient times due to his inventive war machines

Archimedes applied his mathematical knowledge to invent war machines which made him one of the most renowned figures in the ancient west. One of these machines was the Claw of Archimedes which was used to defend the seaside city of Syracuse against an amphibious attack. It consisted of a hook system to lift and topple ships which approached the walls of the city. In 214 BC, during the Siege of Syracuse, the Romans attacked Syracuse with a fleet of 60 warships under Marcellus. The claw machines reportedly sank many Roman ships and threw the attack into confusion. In fact they were so effective that the Romans didn’t know what hit them and wondered whether they were fighting against the Gods. The plausibility of the Claw of Archimedes was tested in a 1999 BBC series and its design was found to be workable.

Claw of Archimedes
Depiction of the Claw of Archimedes


#8 Archimedes was murdered by a Roman soldier despite orders not to kill him

The weapons developed by Archimedes successfully defended Syracuse for a couple of years but the Romans were ultimately victorious in 212 BC. The Roman commander Marcellus was well aware of the genius of Archimedes and he specifically ordered that Archimedes should not be killed. According to legend, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier ordered him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. Enraged by the reply, the soldier killed the 75 year old Archimedes with his sword. The last words attributed to Archimedes are “Nōlī turbāre circulōs meōs!” (“Do not disturb my circles!”), a reference to the work he was doing when disturbed by the soldier. However, there is no reliable evidence to confirm this.

Depiction of Archimedes' death
Depiction of Archimedes being killed by a Roman soldier


#9 A sphere and a cylinder was placed on his tomb on his request

In his work On the Sphere and Cylinder, Archimedes proved that both the volume and the surface area of the sphere were two-thirds that of the cylinder of the same radius. This was his favorite mathematical proof and he was so elated with it that he requested a sculpted sphere and cylinder to be placed on his tomb along with an inscription of the result on the ratio of the two. In 75 BC, 137 years after the death of Archimedes, Roman orator Cicero found his tomb in a neglected condition near the Agrigentine gate in Syracuse. Cicero had the tomb cleaned up and was able to see the carving and the inscription. A tomb discovered in the courtyard of the Hotel Panorama in Syracuse in the early 1960s was claimed to be that of Archimedes but this cannot be established with certainty. His tomb is considered to be lost.

Cicero Discovering the Tomb of Archimedes
Cicero Discovering the Tomb of Archimedes – 1805 painting by Benjamin West


#10 His lost works were rediscovered in 1908 shedding new light on his genius

The works of Archimedes were first compiled into a comprehensive text in 530 AD by Byzantine architect Isidorus of Miletus. A copy of this text was made around 950 AD, again in the Byzantine Empire. This manuscript then made its way to a library in Jerusalem and, ultimately, in 1906, it was discovered by Danish historian Johan Ludvig Heiberg. A leading authority on Archimedes, Heiberg confirmed that the palimpsest included works by Archimedes thought to have been lost. The Archimedes Palimpsest contains two important treatises by Archimedes that can be found nowhere else, The Method and Stomachion. It is now readable after scientific and scholarly work from 1998 to 2008 which used multispectral imaging and an x-ray technique. Archimedes Palimpsest has shed new light on Archimedes including the fact that he anticipated calculus and considered the concept of actual infinity.

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