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Archimedes: Science and Later Years

by Ron Kurtus (revised 19 May 2005)

Archimedes had became a master at mathematics, especially geometry. He spent most of his time working on solving new problems. Sometimes he became so involved in his work that he forgot to eat.

He was not only a great ancient Greek mathematician, but he was also famous for his inventions such as a water pump, levers and pulley, and fire mirrors.

Although his home city Syracuse had been in relative peace for 20 years, the city became part of the effort of Rome to defeat Carthage and rule all of Sicily. Aristotle was killed when the Romans overran his city.

(See Archimedes - Early Years and Mathematics for first part of his life)

Questions you may have include:

This lesson will answer those questions.

Physical science discoveries

The discoveries Archimedes made in the field of mathematics seems to evolve from his love of the subject and basic curiosity concerning geometry. On the other hand, many of his inventions and physical science discoveries were the result of challenges and problems posed by King Hiero.

Method to determine amount of gold

A famous story concerns a time when King Hiero had ordered a gold crown and gave the goldsmith the exact amount of metal to make it. When Hiero received the crown, it had the correct weight but he suspected the goldsmith had substituted some less-expensive silver for gold. Since he could not prove it, he brought the problem to Archimedes.

While pondering the problem, Archimedes entered his bathtub to soak and think about it. When he saw the water rise as he got in, the solution flashed in his mind. The amount of water displaced by a pure gold crown would be different than one of a gold-silver mix. Although their weights could be the same, their volumes would be different.

He jumped from the tub in excitement, ran out of the house naked, and dashed through the streets of Syracuse shouting "Eureka! eureka!" (I have found it!). The fraudulent goldsmith was later brought to justice.

Archimedes principle of hydrostatics

As a result of his discovery in the bathtub, Archimedes developed the basic principles of hydrostatics. He established Archimedes' Principle, which states that the relative weight of a body immersed in a fluid is reduced by the weight of fluid displaced by the body.

He also studied the stability of various floating bodies of different shapes and determined the specific gravity of various materials.

Moving the world

Another time, while dining with King Hiero, Archimedes said, "Give me a place to stand on, and I will move the earth." The king challenged Archimedes to prove the statement.

A large ship had been built in the harbor, but it seemed impossible to launch, no matter how many men pushed on the hull. Archimedes applied the principles of levers and pulleys and built a device that allowed him to use the mechanical advantage of the pulleys to single-handedly move the ship into the water.

Developed weapons

During these years, the political climate around Syracuse was changing. When Archimedes was 46, in 241 BC, the Romans defeated Carthage in the First Punic War. Syracuse initially supported Carthage but later King Hiero agreed to a treaty of alliance with Rome that called for Syracuse to pay tribute and provide grain to the Romans.

Since Syracuse had been threatened by the Romans over the years, King Hiero  persuaded Archimedes to develop weapons to defend the city in case of a possible attack. Archimedes invented a number of clever weapons that would prove effective in defending the city against attacks.


Some of the inventions Archimedes created were catapults to hurl burning balls of fire and grappling cranes to tip over ships. He also proposed making a huge mirror to focus sunlight on the ships to set them on fire.

The fire mirrors

Archimedes invented a system of mirrors that reflected and directed the sun at warships causing them to set fire. It appears that Archimedes actually assembled a group of soldiers with polished shields into a large parabola shape and then focused the reflection from their shields onto the rigging of the ships and igniting them.

Archimedes demonstrating his "fire mirror"

Archimedes demonstrating his "fire mirror"

Final years

When Archimedes was 69, in 218 BC, the Romans and Carthaginians starting to fight the Second Punic War. Under Hannibal, Carthage gained the first round of victories, and his successes in Italy helped convince many of Syracuse that they were allied with the wrong side.

King Hiero honored his treaty with Rome, but when he died in 215 BC, he was succeeded by his 15-year-old grandson Hieronymos, who began negotiations with Hannibal. The following year, the pro-Roman faction within Syracuse had Hieronymos assassinated.

This assassination led to civil war in Syracuse, during which most of Hiero's family was killed. The pro-Carthaginian faction was eventually victorious and took control of the city. Although Archimedes was not involved in politics, he was saddened at the loss of his friends.

Romans attacked Syracuse

The Romans sent Marcus Claudius Marcellus to Sicily to deal with the situation in Syracuse. He first took a nearby city by force and had some 2000 Carthaginian sympathizers beheaded. This savagery following the defeat of a city eliminative any desire to negotiate with Marcellus or the Romans.

Marcellus then attacked Syracuse in 213 BC, both by land and sea. Archimedes was 74 years old at the time.

Used his weapons

The Syracuse army then put the weapons Archimedes had created into action.

Used catapults

Huge catapults hurled 500 pound boulders at the soldiers. Upon capturing Roman soldiers, the Syracuse army beheaded them and catapulted the heads into the ranks of the troops. This completely demoralized the Roman soldiers.

Used the claw

Archimedes had developed a system of large cranes with claws on the end that would lower down on the enemy ships, lift them in the air, and then throw them against the rocks. This lever system scared the Romans so much that the soldiers refused to continue the attack and fled at the mere sight of anything projecting from the walls of the city.

Blockade of city

Marcellus stopped the direct attacks on the city and decided to blockade Syracuse to starve out the city. In 212 BC Marcellus took advantage of the Syracuse's neglect of their defenses during a festival to the goddess Artemis to breach the walls and take the city. Marcellus then gave his soldiers one-day's leave to loot the fallen city.

Archimedes killed

Archimedes was working on a geometry problem and apparently was not aware that the Romans had entered the city. When a Roman soldier came into his room and commanded him to come to with him, Archimedes told him he was too busy on his problem to be bothered. The soldier became enraged, drew his sword and killed him. Archimedes was 75 when he died.


Archimedes spent his life solving mathematical problems. He would often invent devices as a result of solving a problem for the King. His mind and discoveries were truly amazing. Although his weapons of war held off the Romans attacking Syracuse for a while, they ultimately were not enough. A Roman soldier killed a great person.

Lessons learned

Lessons learned from the life of Archimedes include:

You too, can move the world

Resources and references

Ron Kurtus' Credentials


All the Grains of Sand - From Nova

Mathematical Methods of Archimedes

Greek Number Systems

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Top-rated books on Archimedes

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