Archimedes

Archimedes was born around 287 BC in Syracuse on the island of Sicily; ancient sources and modern scholarship identify him as the son of an astronomer named Phidias (or Fidias), and report that he visited Alexandria (Egypt) as a young man to study with the mathematical tradition that followed Euclid before returning to Syracuse to work for most of his life. His surviving writings and later reports portray him as intensely devoted to mathematics and mechanical problems, sometimes losing himself in study and physical experiments. In mathematics Archimedes made breakthrough contributions in geometry and the method of exhaustion (an early form of integration): he computed areas and volumes (notably the area under a parabola and the volume and surface area of a sphere), produced very accurate bounds for π, investigated the Archimedean spiral, and devised notations for very large numbers (notably in The Sand Reckoner). Many historians regard his methods as anticipating integral calculus and credit him as the greatest mathematician before Newton. In physics and engineering he founded much of classical hydrostatics and statics: he enunciated the law of the lever and the law of buoyancy (now called Archimedes’ principle), and he applied mathematical reasoning to practical machines. Archimedes is credited with inventions such as the Archimedean screw (a pump), compound pulleys, siege engines and other devices used in the defense of Syracuse during the Roman siege (accounts vary for some devices, and some descriptions—like the “burning mirrors”—are debated). Archimedes’ life ended during the Roman capture of Syracuse in the Second Punic War (c. 212 BC); multiple ancient accounts state he was killed by a Roman soldier while engaged with a mathematical problem despite orders that he not be harmed. He reportedly regarded his proof that the volume of a sphere is two-thirds that of its circumscribed cylinder as his greatest achievement and requested a carving of a sphere within a cylinder on his tomb.