Archimedes Timeline

Archimedes 17

287 BC Archimedes born in Syracuse c. 287 BC — son of the astronomer Phidias Archimedes was born around 287 BC in the Greek colony of Syracuse on the island of Sicily, then the largest Greek city in the western Mediterranean. His father Phidias was an astronomer. Syracuse was a flourishing hub of commerce, art and science — an ideal birthplace for the ancient world's greatest scientific mind. He may have been related to Hiero II, who would later become King of Syracuse.
287 BC – 212 BC Archimedes of Syracuse The greatest mathematician and engineer of antiquity Archimedes (c.287–212 BC) was a Greek mathematician, physicist, engineer, astronomer and inventor born in Syracuse, Sicily. Son of the astronomer Phidias, he was possibly related to King Hiero II of Syracuse. He is ranked alongside Newton and Gauss as one of the three greatest mathematicians of all time. He left nine surviving treatises covering geometry, hydrostatics, statics and mathematical physics, and invented war machines that held Rome at bay for two years. He died when Roman soldiers breached Syracuse in 212 BC — allegedly while working on a geometry problem.
265 BC – 260 BC Archimedes studies in Alexandria Befriends Eratosthenes and Conon of Samos As a young man, Archimedes travelled to Alexandria, Egypt — the intellectual capital of the Hellenistic world — to study mathematics. There he worked alongside and befriended Eratosthenes of Cyrene (who would later measure the Earth's circumference) and the astronomer Conon of Samos. He immersed himself in the mathematical tradition founded by Euclid. He later dedicated several of his treatises to Conon and Eratosthenes, and his letters to Eratosthenes are among our main sources for his methods.
260 BC Returns to Syracuse — begins work for King Hiero II Engineer and problem-solver to the king After his studies in Alexandria, Archimedes returned to Syracuse and entered the service of King Hiero II, who ruled from 270 to 215 BC. He spent the rest of his life in Syracuse, dividing his time between pure mathematical research — which he pursued for its own sake — and practical engineering solutions for the king. The arrangement would produce some of the most celebrated discoveries in the history of science.
250 BC Archimedes invents the Archimedes screw A helical pump to raise water — still in use today King Hiero II commissioned Archimedes to design the Syracusia, the largest ship in classical antiquity. One problem was pumping bilge water from the enormous hull. Archimedes's solution was the screw pump: a helix inside a hollow cylinder, turned by a handle, which lifts water from a lower to a higher level. The device was so effective that it spread throughout the ancient world for irrigation and drainage. It is still manufactured and used today in water treatment plants and agricultural irrigation across the developing world.
250 BC On the Equilibrium of Planes — law of the lever "Give me a place to stand and I will move the Earth" In his treatise On the Equilibrium of Planes, Archimedes proved the law of the lever mathematically: that weights balance when they are inversely proportional to their distances from the fulcrum. He also identified the concept of the centre of gravity — the single point at which an object's entire weight can be considered to act. To demonstrate the lever's power to King Hiero, he single-handedly hauled a fully loaded merchant ship along the dock using a compound system of pulleys. His famous boast — "Give me a place to stand and I will move the Earth" — captures the principle perfectly.
245 BC Eureka! — Archimedes discovers buoyancy On Floating Bodies: a submerged body displaces its weight in fluid King Hiero II suspected a goldsmith had mixed silver into a supposedly pure gold crown. He tasked Archimedes to test it without destroying it. The solution came to Archimedes while stepping into a public bath — he noticed the water level rose as he entered, and realised that a body displaces a volume of fluid equal to its own volume. Since gold is denser than silver, a silver-adulterated crown would displace more water than a pure gold crown of the same weight. Legend says he leapt from the bath and ran naked through the streets shouting "Eureka!" (I have found it!). He formalised the principle in his treatise On Floating Bodies, the first systematic work in hydrostatics.
240 BC Measurement of a Circle — pi calculated 3 10/71 < π < 3 1/7 — the most precise value for 1,500 years In his Measurement of a Circle, Archimedes calculated pi by inscribing and circumscribing regular polygons around a circle with up to 96 sides, and computing their perimeters. He proved that pi lies between 3 10/71 (≈3.1408) and 3 1/7 (≈3.1429) — the most precise calculation of pi achieved for over 1,500 years. His upper bound of 22/7 remained in widespread use until electronic calculators made arbitrary precision trivial. The method of exhaustion he used anticipates integral calculus.
240 BC The Sand Reckoner Counting grains of sand in the universe — and inventing a number system to do it In The Sand Reckoner, addressed to King Gelo (son of Hiero II), Archimedes set himself the challenge of expressing the number of grains of sand that would fill the entire universe. The Greek number system had no way to express such enormous quantities, so Archimedes invented a new system based on powers of the myriad (10,000), effectively creating the concept of scientific notation. His final estimate was 10^63 grains — remarkably, using Aristarchus's heliocentric model of the universe as the basis for his size estimate. The work also shows Archimedes understood the concept of positional notation two millennia before it became standard.
235 BC On the Sphere and Cylinder The volume and surface area of a sphere — his proudest achievement In his two-volume On the Sphere and Cylinder, Archimedes proved that the surface area of a sphere is 4πr², and that the volume of a sphere is exactly two-thirds the volume of the cylinder that just encloses it. He was so proud of this result that he requested it be engraved on his tomb — a sphere inside a cylinder. When the Roman statesman Cicero visited Syracuse in 75 BC, he found the neglected tomb of Archimedes and confirmed the engraving. The result was not rediscovered by European mathematics until the 17th century.
225 BC On Spirals The geometry of the Archimedean spiral In On Spirals, Archimedes defined and studied the curve now known as the Archimedean spiral — the locus of a point moving at constant speed along a ray that itself rotates at constant speed. He proved results about the areas of regions bounded by spirals and used them to construct a line equal in length to the circumference of a circle — a classical problem of enormous difficulty. The work showed his mastery of geometry as a tool for solving seemingly impossible problems.
225 BC Quadrature of the Parabola The area under a parabola — anticipating integral calculus In Quadrature of the Parabola, Archimedes proved that the area enclosed by a parabola and a straight line is exactly 4/3 the area of the inscribed triangle. He proved this using both a mechanical method (balancing on a lever) and a rigorous method of exhaustion. The result anticipates the fundamental theorem of integral calculus by nearly 2,000 years. Newton and Leibniz both acknowledged the influence of Archimedes's method of exhaustion on their invention of calculus.
220 BC The Method of Mechanical Theorems A secret letter to Eratosthenes — how he actually discovered his results In a letter to Eratosthenes, Archimedes revealed the secret heuristic method he used to discover (but not formally prove) his mathematical results: he imagined slicing geometric figures into infinitely thin strips and balancing them on a lever, using the law of the lever to deduce relationships between areas and volumes. This technique is essentially integral calculus. Archimedes did not consider it rigorous enough for formal proof — he used the method of exhaustion for that — but as a discovery tool, it was 1,800 years ahead of Newton. The work was lost for centuries and only rediscovered in 1906.
214 BC – 212 BC Archimedes' war machines defend Syracuse The Claw, giant catapults and possibly burning mirrors During the siege, Archimedes deployed a series of devastating mechanical devices. His long-range and short-range catapults rained stones and arrows on Roman troops at any distance. The Claw of Archimedes — a crane-like arm with a grappling hook, extended over the city walls — could seize Roman ships, lift them from the water, and capsize or smash them against the rocks. The Roman soldiers became so terrified that if they saw any rope or timber appearing over the walls, they would flee. Ancient sources also mention burning mirrors that focused sunlight onto Roman ships, though modern experiments have produced mixed results. Plutarch wrote that Marcellus retreated and "began to feel that he was fighting against the gods."
214 BC Siege of Syracuse begins Rome attacks — Archimedes defends In 214 BC, the Roman general Marcus Claudius Marcellus besieged Syracuse by sea and land with a fleet of 60 quinqueremes and a large land army. King Hiero II had commissioned Archimedes to prepare the city's defences in anticipation. What followed was one of the most remarkable episodes in military history: a single man's engineering genius held the Roman army at bay for nearly three years.
212 BC Archimedes killed by a Roman soldier Syracuse falls — "Do not disturb my circles" In 212 BC, after a two-year siege, Roman forces breached the walls of Syracuse. Archimedes was working on a geometry problem when a Roman soldier approached and ordered him to come before the general Marcellus. Archimedes refused, saying "Do not disturb my circles." The soldier killed him on the spot. Marcellus was reportedly devastated — he had given orders that Archimedes was not to be harmed, and had admired him greatly. Marcellus arranged for an honourable burial and saw to the welfare of his family. Archimedes was approximately 75 years old.
75 BC Cicero finds the tomb of Archimedes 75 BC — the sphere-in-cylinder engraving confirmed In 75 BC, the Roman statesman and orator Cicero, serving as quaestor in Sicily, went searching for the tomb of Archimedes, which had fallen into neglect and was overgrown with brambles. He found it by the sphere-in-cylinder engraving Archimedes had requested for his tombstone — the proof he was most proud of. Cicero wrote about the discovery with pride, noting that the Romans had allowed the tomb of the greatest mind of antiquity to be forgotten while Syracusans did not even know it existed.