Although Athens had been defeated in the Peloponnesian War and under the clauses of the peace treaty was no longer allowed to have fortifications and a navy, the role of the sea trade - and with it the desire for colonial expansion - was undiminished. In 336 BC the assembly of the cities of the Greek League appointed Alexander III, the king of Macedonia soon to be known as Alexander the Great, generalissimo for the invasion of Asia. The beginning of Alexander's conquest in 334 BC marked the beginning of what has become known as the period of Hellenism (from the Greek "Hellas" = Greece).
When Alexander was 13 years old his father had appointed Aristotle as his teacher. Aristotle was a brilliant scientist, but he, too, fell victim to the racist argument that great intellectual achievements are proof of racial superiority. In his writings on politics Aristotle opposed Plato's position that wise government comes from a philosopher as a ruler; in his view it would be "not merely unnecessary for a king to be a philosopher, but even be a disadvantage, Rather a king should take the advice of true philosophers. Then he would fill his reign with good deeds, not with good words."Aristotle's ideal was the city-state reigned by an educated aristocracy. It was based on the belief of the superiority of the Greeks, who had to use non-Greeks as serfs or slaves to maintain the ideal order. He taught Alexander that as a superior race Greeks should not mingle with others but take all other people as slaves.
Alexander was Macedonian and did not fall for Aristotle's prejudice. He accepted the scientific achievements of Greece and was determined to bring them to all other known civilizations, but he planned to blend all civilizations, not to impose Greek civilization on others. So he embarked on a military campaign to visit and take the capitals of all known civilizations in Asia and Africa and built the largest empire the world had seen to that point in time.
Alexander and his troops marched through Phrygia (in today's Turkey) to Egypt, returned to Mesopotamia to enter Babylon, continued to conquer the Persian empire and arrived at the Indus River. Returning from India he entered Susa, the capital of the ancient Mesopotamian kingdom of Elam, and moved on to set up camp in Babylon again.
To spread the Greek intellectual achievements and blend them with the wisdom of other civilizations Alexander founded more than 70 cities across his empire. In Susa he attempted the fusion of the Greek and Persian civilization through a mass wedding of 10,000 of his soldiers and 80 of his officers with Persian women and took two Persian wives himself. The result was mass desertion and mutiny, one of many that occurred during his campaign.
Alexander was a fiery character and loved banquets of grand scale. In Babylon he fell ill after one such drinking bout and died within 10 days. He was only 33 years old at his death, and his empire fell apart immediately. It was divided amongst his generals. Few of his city foundations survived. The one city that not only survived but rose to become the centre of Greek science was his foundation in Egypt: Alexandria.
After Alexander's death in 323 BC Egypt came under the rule of Ptolemy I, the son of a Macedonian nobleman. Ptolemy had served as Alexander's personal bodyguard and risen to commander of his fleet. He was a wise ruler and did not alienate the Egyptians; on the contrary, he rebuilt the temples of the Pharaohs that had been damaged during a war with Persia and promoted the fusion of the Greek and Egyptian religions.
Ptolemy's invaluable contribution to the history of science was the foundation of the Mouseion (Museum) and Library in the new Egyptian capital Alexandria. To build the base for a world-renowned new university, Ptolemy decreed that visitors to Alexandria were required by law to lend any manuscript in their possession to the library for copying. The law was enforced through regular searches of all ships that entered the port.
Visitors and staff at the Museum and Library received free accommodation and a government salary, without obligation to teach or research other than to participate in debate amongst colleagues. Given that their numbers often went into the hundreds, the support for science must have been a significant part of Egypt's state budget.
Ptolemy's son Ptolemy II continued his father's work, and Alexandria rose to fame around the Mediterranean Sea. No student of philosophy and the sciences could consider himself (and, as we shall see in Lecture 12, herself as well) educated without a stay of several years in the Egyptian capital.
One of the first Greek scientists to study and work in Alexandria was the astronomer Aristarchus of Samos. Only one short manuscript, which discusses the relative sizes of Sun, Moon and Earth, survives from his work. Contemporary reports show, however, that Aristarchos was convinced that the Earth rotates around itself and revolves around the Sun.
The most gifted of Aristarchos' students was Archimedes, who was born around 290 or 280 BC, only 20 years after Ptolemy II. Archimedes lived in the Greek colonial city of Syracuse on Sicily and left it only for short periods. His decision to receive his training in Alexandria shows how rapidly this city attained its standing as the leading intellectual centre.
Archimedes applied mathematics to the treatment of physical problems. Using geometrical methods - the lack of a place-value number system making the direct numerical approach impractical - he derived the exact solution to the problem of the lever. He was also a gifted teacher who could give insightful explanations of physical relationships through simple mathematical demonstrations. His greatest contribution to science is his discovery of the laws of buoyancy.
Archimedes was also the first of the Greek philosopher-scientists to apply his knowledge to problems of practical design. The best known of his numerous inventions is the "Archimedes screw," a device to raise water. The city of Syracuse used his services as a designer of war machinery in the city's defence against Roman attacks. Archimedes' work is probably the first European example of a situation where technology was intricately linked with science.
Another scientist who worked in Alexandria was Eratosthenes of Cyrene. At the time of his birth (around 276 BC) Cyrene had already developed into an intellectual centre of highest reputation, particularly in medicine. But Eratosthenes, who had wide-ranging interests including poetry, theatre and ethics, was first and foremost an astronomer, and Alexandria was the place to go for astronomical studies. So he studied there, and briefly in Athens as well. At the age of about 50 he returned to Alexandria and soon became director of the Library.
Having someone of Eratosthenes' reputation as its director is a clear indication that the Library was not only a book depository but an active research institution. Eratosthenes himself made very accurate observations and is remembered for his determination of the circumference of the Earth.
One century later Alexandria was the place for many of the astronomical observations made by Hipparchus. His observational skills produced some of the most accurate records of the planets and the stars and caused later astronomers to wonder whether he had developed new instruments no longer known today. So accurate were his observations that he determined the length of the year to within 6.5 minutes of today's value. Among his most significant observations was that of the precession of the equinoxes, which indicates movement of the north celestial pole relative to the stars in its vicinity. The effect, explained today as conical movement of the Earth's rotational axis around its mean position, is less than one degree of arc, and to notice it requires a very long observational record. Hipparchus compared his own observations with observations made at Alexandria some 150 years before him and used records from the ancient Babylonian empire to extend his series of data.
The person who established Alexandria's fame as a centre of learning was Eucleides, known to posterity as Euclid. He lived more than 150 years before Hipparchus and worked some 30 years before Eratosthenes was born. We do not know Euclid's birthplace, but it is clearly established that he set up his own School of Mathematics in Alexandria under the reign of Ptolemy I, shortly after the foundation of the Museum and Library.
Euclid is clear proof that with the establishment of Alexandria science had reached the stage where it had become an independent profession. Euclid was quite an average mathematician, but he was a brilliant teacher, probably one of the best the teaching profession has ever seen. Using existing texts from Eudoxus and others he wrote a textbook for his school and called it "Elements of Geometry." The modest title gave no indication of the role this work was going to play in the development of science. Its fame soon spread around the Mediterranean, and wherever science was taught the Elements soon replaced whatever text had been used before. No other text managed to replace it for more than 2000 years. It was translated into Latin, Arabic and several modern European languages and appeared in more than 1000 editions.
In the Elements Euclid put together a compendium of all Greek mathematics known at the time. But he did not only collate texts from several centuries, he reorganized the material, added new proofs and provided commentary in such a way that the discipline of geometry was presented as a cohesive whole.
The Elements demonstrate an important aspect of Greek science: The Greek mathematicians did not develop a place-value number system. The Babylonian place-value number system was lost; China was just developing its decimal place-value system when Alexandria began to flourish, and news of that system did not arrive in Europe until nearly 1000 years later. Greek mathematics therefore did not make big advances in the discipline of arithmetic, where Chinese mathematics excelled. (A full discussion of Chinese science will be presented in Lecture 15.) Instead, Greek mathematicians concentrated on geometry and soon became the leading authorities in that field.
Greek science was rediscovered by Europe during the Renaissance (literally "rebirth" of antiquity). Renaissance scholars were so impressed by the achievements of the Greek scientists that they attempted to give them credit for all intellectual development that occurred under the sun. Writers such as Dasypodius (1593), Erpenius (1613) and Huet (1679) claimed that the Greek civilization invented the place-value number system. The most convincing argument against this falsification of the history of science was provided by the Greek scientists themselves: They would have eagerly exploited the advantages of the place-value system if they would have had knowledge of it. Instead, Archimedes in his work De numero arenae spent much thought on ways to improve the Greek number system to write very large numbers, a trivial problem for anyone accustomed to the use of a place-value number system.
The leading role of Alexandria as a centre for research and learning came to an end when Rome occupied Egypt in 30 BC. Alexandria's Library was damaged a few years earlier during a military confrontation. It had been the largest collection of scientific literature during the period of Hellenism. It was destroyed during a civil war in 272 AD. The small part of the library that could be rescued was placed into a "daughter library", which was destroyed by Christian fanatics in 391 AD.
For 300 years Alexandria had been at the forefront of European science. It had witnessed the period of transition from science as part of philosophy and politics to science as a profession that could support its members as lecturers (as in the case of Euclid) and as consultants and inventors (as in the case of Archimedes).
Alexandria's Museum continued as a place for science with some reputation but lost its innovative edge. Among the scientists who worked at the Museum during Roman times was Sosigenes, who was called to assist Julius Caesar in his calendar reform (described in Lecture 7), and Hero, a mathematician and inventor of amazing ingenuity. The most famous of the Alexandrian scientists of the Roman period was Ptolemy, the great summarizer of Greek astronomy and mathematics who we shall meet in the next lecture.
The following references are all quoted after Ifrah, G. (2000) Universal History of Numbers John Wiley & Sons, New York:
Dasypodius (1593) Institutionum Mathematicarum ... Strassbourg.
Erpenius (1613) Gramattica Arabica. Leiden.
Huet, P. D. (1679) Demonstratio Evangelica. Paris.