Archimedes

Archimedes of Syracuse (c. 287 – c. 212 BC) was an ancient Greek mathematician, physicist, engineer, astronomer, and inventor. Born in the seaport city of Syracuse on the island of Sicily, then a Greek colony, he spent most of his life in the service of King Hiero II. According to tradition, he studied in Alexandria, Egypt, where he encountered the work of Euclid and his successors. Upon returning to Syracuse, he devoted himself to a life of scientific inquiry and practical invention.

Archimedes' mathematical achievements were extraordinary. He used the method of exhaustion to calculate areas and volumes, anticipating integral calculus. In his treatise On the Sphere and Cylinder, he proved that the surface area and volume of a sphere are two-thirds those of its circumscribing cylinder—a result he requested be inscribed on his tombstone. In Measurement of a Circle, he approximated the value of π by inscribing and circumscribing polygons, establishing bounds of 3 10/71 and 3 1/7. The Sand Reckoner introduced a system for representing very large numbers, challenging the notion that the number of grains of sand was infinite. His work The Method of Mechanical Theorems, discovered only in 1906 in the Archimedes Palimpsest, revealed how he used mechanical analogies to arrive at geometric theorems.

In physics, Archimedes founded hydrostatics and statics. His principle of buoyancy, known as Archimedes' principle, states that a body immersed in a fluid experiences an upward force equal to the weight of the fluid displaced. The story of his discovery in the bathtub, leading him to run naked shouting "Eureka!" is recounted by Vitruvius. In On Floating Bodies, he analyzed the stability of floating objects of various shapes. In mechanics, he formulated the law of the lever and the concept of center of gravity, and devised compound pulley systems capable of moving heavy loads with minimal force. He is credited with inventing the Archimedes' screw, a device still used to pump water for irrigation.

As an engineer, Archimedes designed machines to defend Syracuse during the Second Punic War. According to historians such as Plutarch and Polybius, he constructed catapults, grappling hooks to lift and capsize Roman ships, and possibly mirrors to focus sunlight and set ships on fire—though the latter is debated. The Romans, under Marcus Claudius Marcellus, eventually breached the city's defenses, and Archimedes was killed by a Roman soldier despite orders to spare him. Plutarch relates that he was working on a geometric problem and refused to be interrupted.

Archimedes' legacy endured through the preservation of his writings. His works were translated into Arabic and later into Latin, influencing medieval Islamic scholars and European scientists of the Renaissance and Scientific Revolution. Galileo Galilei admired and expanded upon his work in mechanics and hydrostatics. The Archimedes Palimpsest, a manuscript overwritten with a prayer book, revealed lost texts and provided insight into his methods. Today, Archimedes is regarded as one of the greatest mathematicians of antiquity, and his contributions remain central to the history of science.