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.George G. Joseph (2000). The Crest of the Peacock, p. 7-8. Princeton University Press. ISBN 0691006598.

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 early Thalassic Age, but are not easily documented. It is generally believed that Greek traders, scholars, and businessmen brought back to Greece the mathematics of the Babylonians and Egyptians. Between 800 BCE and 600 BCE Greek mathematics generally lagged behind Greek literature, and there is very little known about Greek mathematics from this period.

Greek mathematics proper is thought to have begun when Thales of Miletus (ca. 624 - 548 BCE) and Pythagoras of Samos (ca. 580 - 500 BCE) brought knowledge of Egyptian and Babylonian mathematics to Greece. In Egypt, they were said to have learned geometry. And in Babylon, then under the rule of Nebuchadnezzar, Thales is said to have learned astronomy and to have come in touch with astronomical tables and instruments. 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 Antikythera mechanism, an ancient mechanical calculator.

Archimedes was able to use infinitesimals in a way that is similar to modern integral calculus. By assuming a proposition to be true and showing that this would lead to a contradiction, he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the value of π (Pi). In The Quadrature of the Parabola, Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 times the area of a triangle with equal base and height. He expressed the solution to the problem as a infinite geometric series, whose sum was 4/3. In The Sand Reckoner, Archimedes set out to calculate the number of grains of sand that the universe could contain. In doing so, he challenged the notion that the number of grains of sand was too large to be counted, devising his own counting scheme based on the myriad, which denoted 10,000.

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. For instance, the oldest surviving Latin version of Euclid\'s Elements is a 12th century translation from Arabic.

See also

• Chronology of ancient Greek mathematicians
• History of mathematics
• Timetable of Greek mathematicians

Footnotes and citations

References

• Boyer, Carl B. (1991), A History of Mathematics (Second Edition ed.), John Wiley & Sons, Inc., ISBN 0471543977
• Cooke, Roger (1997), The History of Mathematics: A Brief Course, Wiley-Interscience, ISBN 0471180823
• Derbyshire, John (2006), Unknown Quantity: A Real And Imaginary History of Algebra, Joseph Henry Press, ISBN 030909657X
• Stillwell, John (2004), Mathematics and its History (Second Edition ed.), Springer Science + Business Media Inc., ISBN 0387953361
• Burton, David M. (1997), The History of Mathematics: An Introduction (Third Edition ed.), The McGraw-Hill Companies, Inc., ISBN 0070094659
• Heath, Thomas Little (1981), A History of Greek Mathematics, Volume I, Dover publications, ISBN 0486240738
• Heath, Thomas Little (1981), A History of Greek Mathematics, Volume II, Dover publications, ISBN 0486240746
• Heath, Thomas Little (2003), A Manual of Greek Mathematics, Dover publications, ISBN 048643231-9

External links

• Vatican Exhibit

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