Greek mathematics

Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean.

Periods

Classical Greek mathematics refers to the mathematics studied before the Hellenistic period, when Greek mathematics was mostly limited to the Greek city-states in ancient Greece, Asia Minor, Libya, and Sicily.

Greek mathematics studied from the time of the Hellenistic period onwards (from 323 BC) refers to all mathematics of those who wrote in the Greek language, since Greek mathematics was now not only written by Greeks but also non-Greek scholars throughout the Hellenistic world, which was spread across the Eastern end of the Mediterranean. Greek mathematics from this point merged with Egyptian and Babylonian mathematics to give rise to the latter phase of Greek mathematics known as Hellenistic mathematics. The most important centre of learning during this period was Alexandria in Egypt, which attracted scholars from across the Hellenistic world, including mostly Greek and Egyptian scholars, as well as Jewish, Persian, Phoenician and even Indian scholars.^[1]

Most of the mathematical texts written in Greek were found in Greece, Egypt, Asia Minor, Mesopotamia, and Sicily.

Achievements

Greek mathematics constitutes a major period in the history of mathematics, fundamental in respect of geometry and the idea of formal proof. Greek mathematics also contributed importantly to ideas on number theory, mathematical analysis, applied mathematics, and, at times, approached close to integral calculus.

Well-known figures in Greek mathematics include Pythagoras, a shadowy figure from the isle of Samos associated partly with number mysticism and numerology, but more commonly with his theorem, and Euclid, who is known for his Elements, a canon of geometry for many centuries.

The most characteristic product of Greek mathematics may be the theory of conic sections, largely developed in the Hellenistic period. The methods used made no explicit use of algebra, nor trigonometry.

Origins

Greek mathematics has origins that are presumed to go back to the 7th century BC, but are not easily documented. It is generally believed that it built on the computational methods of earlier Babylonian and Egyptian mathematics, and it may well have had Phoenician influences.

Greek mathematics proper is thought to have begun from the late 500s BC, when Thales and Pythagoras brought knowledge of Egyptian and Babylonian mathematics to Greece. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. Pythagoras stated the Pythagorean theorem and constructed Pythagorean triples algebraically, according to Proclus' commentary on Euclid.

The high period

Mathematical developments took place in Greek-speaking centres as far apart as Egypt and Sicily, and with a high estimation of the intellectual and cultural status of mathematics (for example in the school of Plato). The Sand Reckoner by Archimedes, a resident of Syracuse, bespeaks a man who made major discoveries, and whose originality and accomplishments are commonly reckoned to be on par with those of Isaac Newton and C. F. Gauss.

Greek mathematics and astronomy reached a rather advanced stage during Hellenism, with scholars such as Hipparchus, Posidonius and Ptolemy, capable of the construction of simple analogue computers such as the Antikythera mechanism.

Transmission and the manuscript tradition

Although the earliest Greek language texts on mathematics that have been found were written after the Hellenistic period, many of these are considered to be copies of works written during and before the Hellenistic period. Nevertheless, the dates of Greek mathematics are more certain than the dates of earlier mathematical writing, since a large number of chronologies exist that, overlapping, record events year by year up to the present day. Even so, many dates are uncertain; but the doubt is a matter of decades rather than centuries.

During the Middle Ages, Europe derived much of its knowledge of Greek mathematics via Islamic mathematics. The texts of Greek mathematics were for the most part preserved and transmitted in the Muslim world.