“Eureka!” Archimedes’ Moment of Genius

Some of mankind’s greatest achievements remain shrouded in mystery centuries later. This is the case, for instance, of the Great Pyramids erected by the Egyptians which we barely seem to understand nowadays (and aliens did not take part in building those, but thanks for passing by and saying hi, conspirators).

Surely, science and technology took giant leaps over the Antiquity period. This also happened because some savants shared an enthusiasm for furthering human knowledge and pushed for progress in literally every scientific field. Aristotle, Euclid, Hippocrates, Socrates (among others) have laid the foundation of mathematics, geometry, medicine and philosophy. Without Ancient Greek thinkers, general knowledge games would last about five minutes.

Ever wondered why complex math problems feature Greek letters like alpha (α) or omega (ω)? Because Ancient Greeks were at the forefront of mathematical thinking. You’re welcome.

To put that into more tangible perspective, some of their thousand-year-old inventions still form the pattern of your own daily routines (the following illustrations may not apply depending on your country of residence, please cross out irrelevant answers) with things like democracy, the first alarm clock, the art of theater or the Olympic Games… Ancient Greeks also introduced the first historian, Herodotus – hence the curiosity for history you satisfy reading through this post (thanks, by the way) could be another legacy of their inventiveness.

Nevertheless, given the time it took for the Hellenistic civilization to slowly turn into our Western societies, accounts of scientific breakthroughs in Ancient Greece still lie at the boundary between fact and legend. That is perhaps better exemplified with the story of Archimedes, who lived in Syracuse (Sicily) in the 3rd century B.C.


Before he earned a deserved reputation of brilliant astronomer and mathematician, Archimedes worked at the court of Hiero II, King of Syracuse. Only aged 22, he was personal adviser to the monarch and assisted him in any matter requiring quick-solving skills. This position happened to be a good springboard to his future scientific achievements.

On one occasion, the king ordered a local jeweler to mold a votive crown -a piece of jewelry meant as an offering to the gods- out of pure gold. He then handed the quantity of gold required to do the job to the craftsman, and days later, Hiero received the precious object ceremoniously. (Alike Midas, it seems like Greek monarchs were fascinated by gold-made items.)

But something was not quite right. The king was doubtful about the final result; more specifically, he wondered whether the jeweler had followed his instructions to the letter or not. What if the crown had been made out of gold but also less ‘noble’ metals – especially silver – so that the jewelry maker could retain some of the king’s gold for him?

Syracuse amphiteater
Syracuse, in ruins today. (Photo: Berthold Werner via Wikipedia, CC BY-SA 3.0)

Faced with such insoluble a question, King Hiero looked for advice from his 22-year-old counsellor. He tasked Archimedes with solving the issue and determining whether there had been foul play or not. Most importantly, the young scientist was ordered not to break the crown apart or melt it in an attempt to check its contents – such an offense could cause divine anger.

Despite his fascination for puzzles and riddles, Archimedes stumbled over the problem as he first investigated the issue. But when he went to the public baths days later, he was suddenly struck by the realization that water could be the key to solving the king’s query. Indeed, diving into the steamy waters of the public baths – that was a thing back in the days – he noticed that the water level shot up once he had gotten in. The quantity of water displaced was proportional to the volume of the body placed into it. So he could use a single experiment to figure out whether the crown had been made out of pure gold or some extra, less costly contents had been added.

Statue of Archimedes taking a bath located in Manchester, England. (Photo: Andrew via Flickr)

The scientist knew from experience that silver was less dense than gold. That meant that, for the exact same weight, those two metals did not move the same quantity of water when immersed: silver would sink and raise the water level slightly above gold’s.

Legend has it that a thrilled Archimedes then jumped out of the baths and run naked across the streets of Syracuse, shouting “Eureka!” (“I’ve found it!”). Back home and dressed (much to the relief of the Greek scientific community), he performed the experiment with the dubious votive crown – sinking it into water and measuring the water level – and the amount of gold the monarch had given to mold it. The results were surprising: the crown raised more water in the bath, meaning that it was made using less dense components – some of the king’s gold had been replaced by silver. Archimedes had unmasked the deceptive craftsman.

archimedes and eureka story cartoon
If you missed the point of the last three paragraphs, here’s a funny comic from Margreet de Heer to get it. On a side note, now you know how to defend yourself when charged with indecent exposure: “Sorry, Your Honour, I was only celebrating a scientific breakthrough following an ancient tradition.”

Upon hearing the news, Hiero’s own level of anger probably rose as well, which one would measure by the fate awaiting the tricky jeweler. Unfortunately, no historical evidence accounts for what happened next. Much alike Newton’s apple, this whole episode still raises historians’ eyebrows to this day. (Though the one about Newton is very likely to have occured.)

Whatever the true story behind Archimedes’ brilliant idea was, the principle he came up with became a cornerstone of hydrostatics, reading (take a deep breath):

“The upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.”

The young scientist set off for a brilliant career, making scientific discoveries and perfecting his problem-solving skills in the course of the following fifty years. In 214 B.C., the savant had turned into an old man: he was 73 years old. The city of Syracuse, a long-time ally of the Roman Empire, had reshuffled the diplomatic cards and partnered with Hannibal’s troops under the reign of Hieronymus, Hiero II’s grandson.

Thus the outbreak of the Second Punic War, in the course of which both Rome and Carthage fought one another for control in the Mediterranean, posed a direct threat to Syracuse. Roman legions came in great numbers and laid siege to the city under the command of General Marcellus; thanks to machines designed by Archimedes himself to protect the city, Roman forces were unable to break Syracuse defenses until, two years later, the city eventually fell into Marcellus’ command.

Thomas Ralph Spence, Archimedes Directing the Defenses of Syracuse, 1895. (Photo: Wikipedia)

The latter expressly ordered his men not to harm Archimedes, whom he considered a previous asset for forthcoming military campaigns or from his sheer scientific genius. Nevertheless, when a Roman legionary came across the 75-year-old scientist, he certainly failed to recognize in him ‘sheer genius’. Indeed, Archimedes was kneeling on the ground, drawing geometric shapes in the sand and probably uttering complex mathematical formulas when the soldier asked him to surrender. Legend has it that the old savant got irritated to be disturbed in the course of an experiment, and replied tit for tat: “Do not disturb my circles.” Furious, the legionary then picked up his sword and killed the old man.

The Greek Archimedes underwent a strange fate. His scientific ‘birth’ involved a fake votive crown, a greedy craftsman and a providential bath, while his deathbed was made up sand covered with geometric shapes. He lived and died in the middle of an experiment.




Author: Nicolas

Ingrédients : 33% d'anecdotes insolites, 19% de livres poussiéreux, le reste de curiosité névrosée. Auteur du Petit dictionnaire des sales boulots (Vendémiaire, 2022). Chroniqueur chez Slate et RetroNews.

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