Everywhere you look in ancient Greece, you are sure to find not only pioneers, but forefathers of their fields; famous Greeks who advanced their discipline leaps and bounds, and whose influence can be felt to this day. Medicine had Hippocrates, politics had Solon, history had Herodotus, and philosophy had the likes of Socrates, Plato and Aristotle. When it comes to mathematics, one name stands above all others: Archimedes.


His discoveries and writings shaped mathematical thought for millennia, from his plethora of geometrical findings to his accurate approximation of pi. He experimented with calculus before it even existed and laid out a law of the lever that, he purportedly declared, would allow him to “move the Earth”.

Archimedes’ genius stretched far beyond theory, though. He was an inventor and engineer, who conceived of machines still in use and weapons powerful enough to give the Roman military cause to worry. That is, of course, if all the stories are to be believed.

Who was Archimedes?

As next to nothing is known about the life of Archimedes, stories written by historians long after his death comprise the only biographical information we have – other than his written works, many of which survive only in fragments.

From what can be surmised, Archimedes was born c287 BC in Syracuse, a Greek-speaking city on the south-east coast of Sicily. In one of his works, he named his father as Phidias, an astronomer, but nothing else is known about his family or upbringing.

It is possible that he travelled to Alexandria, Egypt, and studied there for a spell since he seemed to form relationships with the polymath Eratosthenes of Cyrene (chief of the Library of Alexandria, one of the Seven Wonders of the Ancient World) and the astronomer Conon of Samos, a great intellect of the city.

For nearly all of his life, Archimedes lived and worked in Syracuse, often in the employ of the king, which led to perhaps his most famous story.

What was Archimedes’ ‘Eureka moment’ and did it really happen?

According to the first-century BC Roman architect Vitruvius, Archimedes was approached by Hieron (or Hiero) II of Syracuse to determine whether the golden crown that had just been made for the king was, indeed, solid gold. Hieron suspected the goldsmith of substituting silver.

This posed a tricky problem for Archimedes, as he had to reveal the truth without causing any damage to the crown.

Initially stumped for a solution, inspiration finally came to Archimedes when he settled into a relaxing bath: observing how the water rose as he lowered himself into the tub, he realised the answer might lie in water displacement.

The amount displaced was equal to the amount of his body in the water. So astounded was he that he leaped out of the bath and ran down the street, still naked, yelling “Eureka!”, or “I have found it!”

By placing the crown into water and measuring the displacement, Archimedes could work out the volume and, therefore, the density. Gold is denser than silver, so he could compare the results to a solid lump of gold the same weight as the crown.

Eureka, it turned out that the king had been cheated.

While the story is certainly apocryphal, the great mathematician is credited with a significant discovery concerning buoyancy. He just did not necessarily make it while naked in the bath.

Archimedes’ Principle – which states that an object immersed in fluid will be buoyed upwards by a force equal to the weight of the fluid being displaced – secured his reputation as a founding father of hydrostatics, the study of fluids at rest.

What were some of Archimedes’ greatest discoveries and inventions?

Archimedes laid out his Principle on hydrostatics in his work On Floating Bodies, which survives partly in Greek and in a medieval Latin translation.

This was just one of the many solutions to mathematical questions that he got through in his illustrious career. He proved the law of the lever in On the Equilibrium of Planes, and, the work of which he was most proud – On the Sphere and Cylinder – unpicked the relationship between a sphere and a cylinder.

In geometry, Archimedes proved a number of theorems by finding the areas and volumes of an array of shapes, including cones, parabolas and spheres, using methods that would later develop into what became calculus.

The same techniques helped Archimedes reach an approximation for the value of pi between 3.1408 and 3.1429. The true value is 3.14159 (and so on).

As well as mathematics and physics, Archimedes wrote on astronomy too. In The Sand Reckoner, he attempted to calculate the number of grains of sand needed to fill the universe.

He is also credited – in the writings of the great Roman orator Marcus Tullius Cicero and mathematician Pappus of Alexandria – with a device to show the positions of the Sun, Moon and planets. This may be the legendary Antikythera Mechanism, the world’s first analogue computer (and the MacGuffin, dubbed the Archimedes Dial, in the fifth Indiana Jones movie, Indiana Jones and the Dial of Destiny).

Among Archimedes’ inventions are war machines used during the siege of Syracuse, an early odometer (a small cart where a series of gears dropped a pebble in a box every mile) and the so-called Archimedes Screw, a device to draw water upwards.

According to an anecdotal story, it had been invented in conjunction with another of his achievements: the Syracusia, one of the largest ships in antiquity.

Built for the king of Syracuse, it was large enough for more than 1,900 people and featured among its hundreds of rooms a temple, library and gymnasium. But its size increased the risk of leaks in the hull, leading to Archimedes developing the screw to remove water from the lower decks.

In truth, something similar may have existed earlier in Egypt, but it still bears Archimedes’ name and remains in widespread use around the world today.

What did Archimedes do during the Siege of Syracuse?

During the Second Punic War (218-201 BC), Syracuse incurred the wrath of Rome by switching allegiance to Carthage, resulting in what was expected to be a short and straightforward military campaign under the command of general Marcus Claudius Marcellus and Appius Claudius Pulcher.

Yet the siege of Syracuse lasted for two years, from 214-212 BC, thanks in no small part to Archimedes.

As related in The Histories by second-century BC historian Polybius, the mathematician designed a number of weapons and machines to defend the walls of Syracuse from sea attack, including improved forms of the catapult.

Chief among them was the Archimedes Claw, a crane-like contraption with a hook at the end that could be dropped onto Roman ships and lift them out of the water, and his alleged heat ray (also known as the Archimedes Death Ray).

While debate rages over whether this existed at all, the idea was to angle a series of mirrors to focus the Sun’s rays onto the wood of the enemy’s hulls, which would then catch on fire.

How did Archimedes die?

Syracuse did eventually fall to the Romans in 212 BC, while the defenders were distracted with the celebrations of a religious festival.

Marcellus had demanded that Archimedes be taken alive, knowing what his genius could be worth to Rome, but, as the story goes, a soldier approached the mathematician while absorbed in some calculations.

With his mind elsewhere, he failed to heed what the soldier was saying, and the angered Roman stabbed and killed him.

Where is Archimedes’ tomb?

Today, visitors to the Parco Archeologico della Neapolis in Syracuse will be able to visit what’s called the ‘Tomb of Archimedes’.

However, this is not where the great man was buried, but rather a Roman construction from a couple of centuries later. Archimedes’ true resting place was lost to time, neglected and left to decay.

That said, the Roman statesman and orator Cicero claimed he discovered its whereabouts while serving as an official in Sicily.

He knew it to be the right place from the stone adornments of a sphere and cylinder, placed there in honour of Archimede’s mathematical achievements. Cicero had the tomb restored, but again it would be lost over time.

How has Archimedes' legacy changed over history?

Despite his contributions both in the realms of mathematical theory and in defensive weaponry, Syracuse quickly forgot Archimedes after his death (which goes to explain how his tomb became lost).

It is not known if he had children, or followers, but there is little evidence to suggest that anyone took up the mantle of carrying on his work.

Only in the sixth century AD did Archimedes’ legacy start to be formed when Isidore of Miletus, an architect on the Hagia Sophia, compiled his works for the first time.

Then Eutocius of Ascalon wrote commentaries on Archimedes, which were translated into Arabic in the eighth and ninth centuries, bringing the great mathematician of Syracuse to the attention of the great mathematicians of medieval Islam.


Archimedes’ reputation would flourish, making him a constant source of inspiration during the Middle Ages, the Renaissance and the Scientific Revolution.


Jonny Wilkes
Jonny WilkesFreelance writer

Jonny Wilkes is a former staff writer for BBC History Revealed, and he continues to write for both the magazine and HistoryExtra. He has BA in History from the University of York.