**TEXT SEVEN**

THE ALEXANDRIAN SCHOOL OF MATHEMATIC

Most people think of ancient Greece in terms of the 3rd, 4th and 5th century B.C. The "golden age" when the empire was at its height and the greatest artists, poets and writers lived, was the 5th century B.C. But the giants in maths came later, Eudoxus about 350 B.C., and Euclid, Archimedes and Apollonius between 300 and 200 B.C. The greatest math centre of ancient world was neither Crotone nor Athens but Alexandria. It is with Alexandria that the names of Euclid, Archimedes, Apollonius, Ptolemy, Heron, Pappus, Hypatia, Diophantus, Hipparchus, etc. are connected.

For at least four thousand years the civilization of Egypt followed a rigid pattern. In religion, maths, philosophy, commerce, and argiculture each man imitated his forefathers. No external influence disrupted the calm life and fixed ways. Then, about 325 B.C. Alexander the Great conquered this vast land as well as Greece and the Near East. He founded the city of Alexandria and moved the capital of the ancient world from Athens to this new city. From a fusion of cultures, centered at Alexandria, a new civilization appeared and made its very significant and distinctive contribution to maths and to Western civilization. Two factors vitally influenced the character of the culture of Alexandria: the commercial interests of the Alexandrians with their geographical and navigational problems and the fact that the scholars became involved in the problems facing the people at large. Alexandria became the center of the entire ancient world, for it was ideally located at the junction of Asia, Africa and Europe. On the streets of the city native Egyptians met and traded with Greeks, Persians, Syrians, Romans and Arabs. No city in the world ever embraced such a variety of peoples. It was to this important center that traders and businessmen from all corners of the world directed their routes.

One must not forget that credit for making Alexandria the intellectual centre of the new world does not go to the founder of the city, who died while still engaged in conquests, but to the very capable Ptolemy the First, the general who took over control of Egypt on the death of Alexander. Aware of the cultural importance of the great Greek schools such as those founded by Pythagoras, Plato and Aristotle, Ptolemy decided that Alexandria should have such a school and that it should become the center of Greek culture in this new world. He built a home for the Muses and adjacent to this museum Ptolemy erected a library not only for the preservation of important manuscripts but also for the use by the general public. This famous library at one time contained 750,000 volumes. Together with the museum, the library resembled a modern university, though no university of today can boast of possessing as many great intellects as were assembled there. Today, however, not the slightest trace remains of the famous library and museum and even their exact locations are merely conjectural.

Scholars of all countries were invited to Alexandria by Ptolemy and were supported by grants from him. Consequently, there gathered at this museum poets, philosophers, philologists, astronomers, geographers, physicians, historians, artists, and the most famous mathematicians of the Alexandrian age. The principal group of the scholars gathered at the museurn was Greek, but distinguished members of many other nations also settled there. Among the non-Greeks the most celebrated was the learned Egyptian astronomer, Claudius Ptolemy. One can hardly doubt, of course, that maths had a most important place in the Alexandrian world, but it was not the maths that the classical Greek scholars knew. The civilization of Alexandria developed a kind of maths almost opposite in character to that produced by the classical Greek age. The new maths was practical: while the former was entirely unrelated to application, the latter measured the distance to the farthest stars, enabled men to travel over land and sea, etc. The great Alexandrian mathematicians Archimedes, Hipparchus, Ptolemy, Heron, Menelaus, Diophantus, etc. though they did display almost without exception the Greek genius for theoretical abstractions, nevertheless, they were quite willing to apply their talents to the practical problems necessarily important in their civilization. The man whose work best epitomizes the character of the Alexandrian age is Archimedes, one of the greatest intellects of antiquity.

In the field of maths proper the Alexandrians created and applied methods of indirect measurement. One ought not to underestimate this contribution of the Alexandrians. Their formulas for areas and volumes surprisingly are not in Euclid's Elements for though Euclid lived at the beginning of the Alexandrian age, his goal and the subject matter was really the summation and culmination of the maths of the classical period. Euclid's work is a monument both in original or in any epitome. As far as the Alexandrian age is concerned, the supreme achievement of the Alexandrians was the creation of the most accurate and most influential astronomical theory of ancient times developed by Hipparchus and Claudius Ptolemy.

Unfortunately, the intellectual life of the Greeks was cut short by political events beyond the control of mathematicians and philosophers. The Romans rolled over the Italian peninsula and then began to attack other lands bordering the Mediterranean. The fire swept in from the sea destroyed the great library (47 B.C.) at Alexandria. Two and a half centuries of book collecting and half a million manuscripts were wiped out. The fire at Alexandria was symbolic of the Roman contempt for abstract knowledge. The Romans were practical people and they boasted of their practicality. They left no worthy imprint in the history of maths. Though the museum of Alexandria and the great library were destroyed and the scholars dispersed, Greek science eventually re-emerged, Greek culture did survive, and Europe did learn a lot from the Greeks.

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