Archimedes
Ancient Greek mathematician and inventor of Syracuse.
Archimedes of Syracuse (c. 287 – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor born in the Sicilian city of Syracuse. Very little is known about his personal life, but his surviving work marks him as a major figure in classical science and one of history's greatest mathematicians. He foreshadowed modern calculus and analysis by using infinitesimals and the method of exhaustion to prove geometric theorems, such as the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, and the volumes of segments of paraboloids and hyperboloids of revolution, as well as the area of a spiral.
Beyond geometry, Archimedes approximated pi, studied the spiral that now bears his name, and created a system using exponents to express enormous numbers. He was among the first to apply mathematics to physics, particularly in statics and hydrostatics. He proved the law of the lever, made extensive use of the center of gravity, and stated the principle of buoyancy known as Archimedes' principle. In astronomy, he measured the Sun's apparent diameter and the size of the universe. He is said to have built a planetarium showing the motions of known celestial bodies, possibly a forerunner of the Antikythera mechanism. He also designed practical machines, including the screw pump, compound pulleys, and defensive war engines to defend Syracuse from attack.
Archimedes died during the siege of Syracuse, killed by a Roman soldier despite orders to spare him. The Roman orator Cicero later visited his tomb, which was marked by a sphere and a cylinder—the shape Archimedes had requested to represent his favorite mathematical discovery.
His mathematical writings were not widely known in antiquity. Alexandrian scholars read and cited him, but the first full collection wasn't assembled until around 530 AD by Isidore of Miletus in Byzantine Constantinople. Commentaries by Eutocius in the same century made his work accessible to a broader audience. In the Middle Ages, Archimedes' works were translated into Arabic in the 9th century and into Latin in the 12th, becoming influential during the Renaissance and the Scientific Revolution. The 1906 discovery of the Archimedes Palimpsest revealed new insights into his methods.
The details of his life are obscure. A biography attributed to his friend Heraclides Lembus has been lost, and modern scholars doubt it was actually written by Heraclides. Based on a statement by the Byzantine scholar John Tzetzes that Archimedes lived 75 years before his death in 212 BC, he was likely born around 287 BC in Syracuse, then a self-governing colony in Magna Graecia. In his work *The Sand-Reckoner*, he names his father as Phidias, an astronomer otherwise unknown. Plutarch claimed Archimedes was related to King Hiero II of Syracuse, but Cicero and Silius Italicus suggested he came from humble origins. It is unknown if he married, had children, or visited Alexandria in his youth. His surviving works, addressed to Dositheus of Pelusium (a student of the Alexandrian astronomer Conon of Samos) and to the librarian Eratosthenes, indicate he had collegial ties with scholars there. In the preface to *On Spirals*, he notes that "many years have elapsed since Conon's death," placing Conon's life around 280–220 BC and suggesting Archimedes was older when writing some works.
One famous story involves a golden wreath commissioned by King Hiero II. According to Vitruvius, writing two centuries later, the king suspected a goldsmith had mixed silver into the wreath and kept some gold. Archimedes was asked to investigate. While stepping into a bath, he noticed the water level rose as he sank in, and realized this could measure the wreath's volume. Excited, he ran naked through the streets shouting "Eureka!" ("I have found it!"). He then took lumps of gold and silver equal in weight to the wreath, placed each in water, and showed the wreath displaced more water than the gold but less than the silver, proving it was an alloy. A different account in the 5th-century Latin poem *Carmen de Ponderibus* describes placing the lumps on a balance and immersing the whole apparatus in water; the difference in density caused the scale to tip accordingly.
- field
- Mathematics, physics, engineering, astronomy, invention
- nationality
- Ancient Greek (Syracusan)
- known_for
- Archimedes' principle, law of the lever, approximation of pi, Archimedean spiral, war machines, screw pump
Lore & Background
His father's name was Phidias, an astronomer about whom nothing else is known. Plutarch wrote that Archimedes was related to King Hiero II, though Cicero and Silius Italicus suggest he was of humble origin. It is unknown whether he ever married, had children, or visited Alexandria, though his surviving works addressed to Dositheus of Pelusium and Eratosthenes of Cyrene suggest collegial relations with scholars there. Archimedes is credited with solving the 'golden wreath problem' for King Hiero II. According to Vitruvius, while stepping into a bath, Archimedes noticed the water level rose and realized this could determine the crown's volume, leading him to run naked through the streets crying 'Eureka!' A different account in the Carmen de Ponderibus describes using a balance immersed in water, applying the hydrostatic principle now known as Archimedes' principle. He also designed the huge ship Syracusia and, according to Plutarch, boasted he could move any large weight, using a block-and-tackle pulley system or a windlass. During the Siege of Syracuse, he oversaw war machines that greatly delayed the Roman army under Marcus Claudius Marcellus. Archimedes died during the siege when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting his tomb, which was surmounted by a sphere and a cylinder that Archimedes requested to represent his most valued mathematical discovery.
Reader's Guide
Archimedes’ mathematical writings saw limited circulation during his lifetime and in the centuries immediately following, though scholars in Alexandria did read and cite his works. The first comprehensive collection of his writings was not assembled until the Byzantine era, when Isidore of Miletus compiled them in Constantinople; around the same time, commentaries by Eutocius made these texts accessible to a broader audience for the first time. During the Middle Ages, Archimedes’ works were translated into Arabic in the 9th century, and later into Latin in the 12th century, providing a crucial foundation for thinkers of the Renaissance and the Scientific Revolution. The discovery of the Archimedes Palimpsest in 1906 revealed previously unknown works that shed light on his methods for deriving mathematical results. His legacy rests on a series of fundamental contributions: he anticipated modern calculus through the use of infinitesimals and the method of exhaustion to prove theorems on the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, and the volumes of segments of paraboloids and hyperboloids, as well as the area of a spiral. He also derived an approximation of pi, defined the Archimedean spiral, and devised a system using exponentiation to express very large numbers. In physics, he applied mathematics to statics and hydrostatics, proving the law of the lever, developing the concept of center of gravity, and enunciating the law of buoyancy now known as Archimedes’ principle. His engineering inventions include the screw pump, compound pulleys, and defensive war machines for Syracuse. In astronomy, he measured the apparent diameter of the Sun and the size of the universe, and is said to have built a planetarium device that modeled celestial movements, possibly a precursor to the Antikythera mechanism. His principles remain central to modern science and mathematics education.
Did You Know?
- Archimedes derived an approximation of pi and defined the Archimedean spiral.
- He devised a system using exponentiation for expressing very large numbers.
- He is said to have built a planetarium device that demonstrated movements of celestial bodies, possibly a precursor to the Antikythera mechanism.
Common Misconceptions (Editorial)
- A common misconception is that Archimedes invented the principle of buoyancy (Archimedes’ principle) solely from the "Eureka!" bath story. While that anecdote from Vitruvius is famous, a different ancient account in the Carmen de Ponderibus describes him using a balance immersed in water to solve the golden wreath problem.
- Some assume Archimedes was a pure mathematician with no practical engineering role. In fact, the facts record that he designed the massive ship Syracusia, oversaw war machines during the Siege of Syracuse, and claimed he could move any large weight using pulleys or a windlass.
- It is often thought that Archimedes visited Alexandria and studied there. However, the facts state it is unknown whether he ever visited Alexandria, though his works addressed to scholars like Dositheus and Eratosthenes suggest collegial relations.
Why It Matters (Editorial)
Archimedes endures as a symbol of the fusion of abstract mathematics with tangible invention, from his rigorous proofs anticipating calculus to his legendary war machines. His legacy reminds us that the most profound scientific insights—like the law of the lever or the principle of buoyancy—can arise from everyday observations, and that a single mind can shape both theoretical knowledge and practical engineering for millennia.
Notable Quotes (Wikiquote)
"Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, philosopher, scientist and engineer." — Archimedes "I have found it! or I have got it!, commonly quoted as Eureka!" — Archimedes "Give me the place to stand, and I shall move the earth." — Archimedes "Give me a place to stand and with a lever I will move the whole world." — Archimedes
Frequently Asked Questions
Who is Archimedes?
Archimedes was a polymath from Syracuse in Sicily who lived in the third century BC. He worked across mathematics, physics, engineering, and astronomy, making him one of the most influential thinkers of the ancient world.
What are Archimedes's key contributions?
He developed the method of exhaustion to rigorously prove geometric theorems and anticipated ideas that would later become calculus. He also formulated the principle of buoyancy, the law of the lever, and produced a close approximation of pi.
Why is Archimedes important to the history of invention?
His work bridged pure mathematics and practical engineering, showing that rigorous proof could drive real-world machines and tools. He is widely regarded as one of the greatest mathematicians who ever lived and a foundational figure in classical science.
What did Archimedes invent for the defense of Syracuse?
He designed war machines such as the Archimedean screw pump, defensive catapults, and a giant claw to lift and capsize attacking ships. These devices helped Syracuse resist the Roman siege for years despite being vastly outnumbered.
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