It is known that Archimedes spent some of his life in Alexandria, the center of scientific activity during his era. It was in Alexandria that Ptolemy I Soter (died 283 B.C.) invited a circle of philosophers and literary men from Greece to study. He founded the "Museum" and "Library" an academy where arts and sciences were cultivated. Scholars from Greece, Babylonia, and Rome gathered to study under the professors of the "Museum" 

Among the sciences cultivated in Alexandria were geometry, algebra, trigonometry, astronomy, astrology, geography, surveying, mechanics, and alchemy. The Alexandrians were generally specialists straying away from the old Greek philosophy that "all learning" is province ².

One of the first of the famous Alexandrian scholars was Euclid with his Elements of Geometry and it is suspected that while Archimedes was in Alexandria he studied with the pupils of Euclid. It is also assumed that while in Alexandria Archimedes became friends with the Conon of Samos and with Eratosthenes. It was to Conon that he sent his discoveries before publication, and after the death of Conon to Dositheus of Pelusium, the friend and pupil of Conon. Through Eratosthenes Archimedes introduced the Cattle Problem to the mathematicians of Alexandria, and it was for Eratosthenes that Archimedes wrote the Method ³.

Upon his return to Syracuse from Egypt, Archimedes devoted his life to the study of mathematics. He felt that his mechanical inventions, which were in fact what provided him with his fame, were merely the diversions of a geometer at play". In Plutarch's words, "he possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge that , though these inventions had obtained for him the renown of more than human sagacity, he yet would not deign to leave behind him any written work on such subjects, but regarding as ignoble and sordid the business of mechanics and every sort of art which is directed to use and profit." ⁴  Because of this belief, Archimedes wrote only on strictly mathematical subjects, with the exception of one work, On Sphere Making. It is the assertion of Pappus that this work is a description of the construction of a devise composed of concentric glass spheres, moved by water power, representing the apparent motions of the planets, moon, sun, and perhaps the constellations. It was said by Cicero that Marcellus took as booty from the sack of Syracuse an instrument of this type. ⁵

It seems that it was the devotion to Hieron that induced Archimedes to divert his mathematical studies to his engineering skills. There are many "stories" of Archimedes' achievements in this field that are difficult to substantiate but many indicate that the inventions were created at Hieron's request. A well published story by Vitruvius is that of Hieron's desire to know if all the gold he had given to a goldsmith to create a crown was actually used instead of being substituted with an amount of silver. 

The story says that the problem was presented to Archimedes causing considerable puzzlement. While pondering the problem he visited a public bath and noticed that the water in the tub rose in proportion to the amount that he immersed his body into it. This indicated a solution to the problem because Archimedes observed that by noting the difference in overflow when the crown and equal weights of gold or silver were immersed he would be able to distinguish if the crown were of pure gold.

Another story according to Pappus relates to Archimedes' famous statement, "Give me a place to stand, and I can move the earth", that resulted from his discovery to the solution of the problem, To Move a Given Weight by a Given Force, presented to him by Hieron.

Plutarch also tells the story in his Life of Marcellus ⁷ , stating that Archimedes declared to Hieron that he could move any given weight with any given force and that if he were given another Earth to move to he would move this one. With this Hieron requested a demonstration whereby Archimedes attached a system of block and tackle (other accounts by Athenaeus indicate that a helix was used, this is a machine consisting of a cog-wheel with oblique teeth moving on a cylindrical helix turned by a handle) to a fully laden vessel that had been drawn ashore by many men and proceeded to move the vessel along smoothly and safely from a great distance by merely pulling with one hand on the device. 

It was this same ship that Hieron had built as a gift to King Ptolemy, but the combined force of the population of Syracuse was unable to launch it. At this, Archimedes invented a device that enabled Hieron to launch the ship on his own, whereby Hieron proclaimed, from that day forth Archimedes was to be believed in everything that he might say." ⁸

Another of Archimedes' inventions is the Archimedes Screw , or water screw , as it is also known. This device consists of a screw within a tightly enclosing box that is used to draw water. Its origin is believed to be in in ancient Egypt where it was, and still is, used to irrigate fields. It was also thought to be used to pump the bilges of Hieron's ships. In The Ten Books on Architecture,  De Architectura  , Book X , Chapter 6 , The Water Screw , the ancient Roman engineer and historian,  Vitruvius, explains the design and construction of the Archimedes Screw . 

Archimedes was 75 at the time and personally directed the defense of Syracuse. An account of the siege of Syracuse is given in Plutarch's Life of Marcellus. In his account, Plutarch tells of a system of both catapult and  crossbow with selective ranges allowing for a continuous assault on the Romans regardless of their range from the city. Other defenses included Archimedes claw , consisting of long poles that dropped large weights through the Roman ships and cranes that grappled the ship,  lifting them from the water and then dropping them stern first back into the sea.⁹

Plutarch states that Marcellus scorned his own engineers, stating, "shall we not make an end of fighting against this geometrical Briareus who, sitting at ease by the sea, plays pitch and toss with our ships to our confusion, and by the multitude of missiles that he hauls at us outdoes the hundred-handed giants of mythology. But this had little effect on them since the Romans were in such terror that if they did see a piece of rope or wood projecting above the wall, they would cry there it is again," declaring that Archimedes was setting some engine in motion against them, and would turn their backs and run away, insomuch that Marcellus desisted from all conflicts and assaults, putting all his hope in a long siege." ¹⁰

In his death, history relates, Archimedes was absorbed in mathematical contemplation. After a two year siege of Syracuse , the Romans temporarily withdrew their forces creating an air of overconfidence amongst the Syracuse population. During a religious festival, Pro-Roman sympathizers led the Roman forces to the weak points in the defenses, enabling them to overrun the city. Marcellus gave specific orders to spare the life of Archimedes, but in the confusion of the sack of the city, he was slain by a common soldier. ¹¹  It is here that many different accounts of Archimedes' death are given. 

The other versions of the story are similar with the most colorful quoting Archimedes as saying, "Stand away, fellow, from my diagram," causing rage in the soldier. In his grief for the death of such a noble person, Marcellus erected an elaborate monument in Archimedes' honor and directed that he be honored with a burial. As requested by Archimedes, his friends and relatives placed on his tomb a representation of a cylinder circumscribing a sphere within it and an inscription stating the relationship between the two bodies (the volume of a sphere is equal to two thirds that of the circumscribing cylinder). From this, it can be inferred that Archimedes considered this his greatest achievement.

Centuries later,  Archimedes's tomb was found in a neglected state and identified because of the inscription by the Roman orator Cicero. Cicero restored the tomb stating in disgust, "And thus one of the noblest cities of Greece, once indeed a very great seat of learning, would have been ignorant of the monument of its most brilliant citizen, except that it was revealed by a man of Arpinum." ¹¹

Archimedes: A Biography excerpted by permission from "The History of Mathematics" by John C. Blewett © 1992

1.  T.L. Heath, The Works of Archimedes, with a supplement The Methods of Archimedes as discovered by Heiberg, (New York: Dover Publications, 1912), p. xv

2.  Justus Schifferes, "The Alexandrian School," The Book of Popular Science, September 1956, p.355

3. Robert Maynard Hutchins, Editor in Chief, Great Books of the Western World, II. Euclid, Archimedes, Apollonius of Perga, Nicomachus, (Chicago: Encyclopedia Britannica, Inc., 1952), p. 399

4. Heath, p. xvi

5. Marshall Clagett, “Archimedes," Collier s Encyclopedia, Volume 2, 1988

6. "Archimedes," Encyclopedia Britannica, Inc., Volume 2, 1972

7. Clagett, p.479

8. Heath, pp. xix, xx

9. David M. Burton, The History of Mathematics, An Introduction, Second Edition, (Iowa: Wm. C. Brown Publishers, 1991), p. 206

10. Heath, p.xvii

11. Burton, p. 206