Roman historians have related many picturesque stories about Archimedes. Among these are the descriptions of the ingenious  contrivances devised by Archimedes to aid the defense of Syracuse against the siege directed by the Roman general Marcellus. There were catapults with adjustable ranges, movable projecting poles for dropping heavy weights on enemy ships that approached too near the city walls, and great grappling cranes that hoisted enemy ships from the water. The story that he used large burning-masses to set the enemy’s vessels on fire is of later origin, but could be true.

There also is the story of how he lent credence to his statement, “Give me a place to stand on and I will move the Earth,” by effortlessly and single-handedly moving, with a compound pulley arrangement, a heavily weighted ship that had been drawn up by a large contingent of workers only with great difficulty.

Apparently Archimedes was capable of strong mental concentration, and tales are told of his obliviousness to his surrounding when engrossed by a problem. The frequently told story of King Hieron’s crown and the suspected goldsmith is typical. It seems that King Hieron had a goldsmith fashion him a crown from a given weight of gold. Fearing that the goldsmith may have replaced some of the gold by hidden silver, and not wanting to cut the crown apart to find out, the King referred the matter to Archimedes, who, when in the public baths one day hit upon a solution by discovering the first law of Hydrostatics-that a body when immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. In his excitement, forgetting to clothe himself, he rose from his bath and ran home through shouting, “Eureka! Eureka!” (I have found it! I have found it!) He placed the crown on one pan of a balance and an equal weight of gold one the other, and set the whole thing underwater. The pan containing the crown rose, showing that the crown contained some spurious materials less dense than gold. The Eureka can we have today to measure volumes of irregular solids got its name from this story!

Archimedes worked much of his geometry from figures drawn in the ashes of the hearth or in the after-bathing oil smeared on his body. In fact, it is said that he met his end during the sack of Syracuse, while preoccupied with a diagram drawn on a sand tray. According to one version, he ordered a pillaging Roman soldier to stand clear of his diagram, whereupon the incensed looter ran a spear through the old man.

Due to Archimedes’ defense machines, Syracuse resisted the Roman siege for close to three years. The city’s defenses were finally broken only when, during a celebration within the city, the overconfident Syracusans relaxed their guard. Marcellus had built up an immense respect for his ingenious adversary, and when he finally breached the city walls, he gave strict orders that no harm should come to the illustrious mathematician. Marcellus’ affliction was very great upon hearing of Archimedes’ death, and with all due honor and veneration, he buried the famous scholar in the city cemetery. Archimedes , justly proud of one of his great geometrical discoveries, requested that a sphere and a circumscribed right circular cylinder be engraved upon his tombstone. Marcellus saw to it that his request was carried out.

Many years later, in 75B.C., when Cicero was serving as a Roman Quaestor in Sicily, he inquired as to the whereabouts of  Archimedes’ tomb. To his surprise, the Syracusans knew nothing of it. With considerable effort Cicero examined all the monuments in the cemetery, of which there were a great many. Finally he noticed a small column, standing out a little above the overgrown briars and shrubs, with the figure of a sphere and a circumscribed cylinder upon it. Thus, the long-neglected and forgotten tomb of the greatest of all Syracusans was found. Cicero had men with scythes clear away the brush, and he left orders that the surrounding grounds be thenceforth preserved. How long this respect was kept up we do not know, for again the tomb completely vanished into the mists of time. Then, in 1965, while excavating for the foundations of a hotel in Syracuse, the steam shovel came up carrying a tombstone with a sphere and circumscribed cylinder engraved upon it. Thus the long-vanished tomb was found once again.

Referring to the death of Archimedes, Sir William Rowan Hamilton once remarked, “Who would not rather have the fame of Archimedes then that of his conqueror Marcellus?”, and in the same vein Alfred North Whitehead commented, “No Roman ever died in contemplation over a geometrical diagram.” The twentieth-century English mathematician G. H. Hardy said, “Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.” Voltaire had similarly remarked, “There was more imagination in the head of Archimedes than in that of Homer.”

The works of Archimedes are masterpieces of mathematical expositions and to a remarkable extent resemble modern journal articles. They are written with a high finish and an economy of presentation and exhibit great originality, computational skill , and rigor in demonstration. About ten treatises have come down to us, and there are various traces of lost works. Probably the most remarkable contribution made to mathematics in these works is the early development of some of the methods of the integral calculus.

Three of Archimedes’ extant works devoted to plane geometry. They are the Measurement of a Circle, Quadrature of the Parabola, and On Spirals. Two of Archimedes’ extant works are devoted to geometry of three dimensions, namely, On the Sphere and Cylinder and On the Conoids and Spheroids.

Archimedes wrote two related essays on arithmetic, one of which is lost. The extant paper entitled The Sand Reckoner, is addressed to Gelon, son of King Hieron. It is here, among related remarks pertaining to Astronomy, that we learn that Aristarchus (310-230B.C.) had put forward the Copernican Theory of the Solar System. In addition to the two arithmetic essays there is the so-called Cattle Problem which, from a salutation, appears to have been communicated by Archimedes to Eratosthenes.

Archimedes has also been credited with a lost work On the Calendar and another lost work On Sphere Making. In the latter, Archimedes described a planetarium that he constructed to show the motion of the sun and, the five known planets of his day. The mechanism probably was operated by water. Cicero actually saw the mechanism and gave a description of it. The Loculus Archimedius, a teasing puzzle composed of fourteen assorted polygonal pieces to be assembled into a square, in all likelihood was not designed by Archimedes, and probably received its name merely as a way of expressing the puzzle is clever and difficult.

Archimedes’ best known mechanical invention is the water-screw, devised by him for irrigating fields, draining marshes, and emptying water from holds of ships. It is still used in Egypt today.