The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and beehive tombs, they left behind no mathematical documents.
Though no direct evidence is available, it is generally thought that the neighboring Babylonian and Egyptian civilizations had an influence on the younger Greek tradition. Unlike the flourishing of Greek literature in the span of 800 to 600 BC, not much is known about Greek mathematics in this early period—nearly all of the information was passed down through later authors, beginning in the mid-4th century BC.
Greek mathematics allegedly began with Thales of Miletus (c. 624–548 BC). Very little is known about his life and works, although it is generally agreed that he was one of the Seven Wise Men of Greece. According to Proclus, he traveled to Babylon from where he learned mathematics and other subjects, and came up with the proof of what is now called Thales' Theorem.
An equally enigmatic figure is Pythagoras of Samos (c. 580–500 BC), who supposedly visited Egypt and Babylon, and ultimately settled in Croton, Magna Graecia, where he started a kind of cult. Pythagoreans believed that "all is number" and were keen in looking for mathematical relations between numbers and things. Pythagoras himself was given credit for many later discoveries, including the construction of the five regular solids. However, Aristotle refused to attribute anything specifically to Pythagoras and only discussed the work of the Pythagoreans as a group.
Greek mathematics also drew the attention of philosophers during the Classical period. Plato (c. 428–348 BC), the founder of the Platonic Academy, mentions mathematics in several of his dialogues. While not considered a mathematician, Plato seems to have been influenced by Pythagorean ideas about number and believed that the elements of matter could be broken down into geometric solids. He also believed that geometrical proportions bound the cosmos together rather than physical or mechanical forces.Aristotle (c. 384–322 BC), the founder of the Peripatetic school, often used mathematics to illustrate many of his theories, as when he used geometry in his theory of the rainbow and the theory of proportions in his analysis of motion. Much of the knowledge known about ancient Greek mathematics in this period is thanks to records referenced by Aristotle in his own works.
Hellenistic and Roman periods
A fragment from Euclid's Elements (c. 300 BC), widely considered the most influential mathematics textbook of all time.
Greek mathematics and astronomy reached its acme during the Hellenistic and early Roman periods, and much of the work represented by scholars such as Euclid (fl. 300 BC), Archimedes (c. 287–212 BC), Apollonius (c. 240–190 BC), Hipparchus (c. 190–120 BC), and Ptolemy (c. 100–170 AD) was of a very advanced level. There is also evidence of combining mathematical knowledge with technical or practical applications, as found for instance in the construction of simple analogue computers like the Antikythera mechanism, in the accurate measurement for the circumference of the Earth by Eratosthenes (276 – 194 BC), or in the mechanical works of Hero (c. 10–70 AD).
Several Hellenistic centers of learning appeared during this period, of which the most important one was the Musaeum in Alexandria, Egypt, which attracted scholars from across the Hellenistic world (mostly Greek, but also Egyptian, Jewish, Persian, Phoenician, and even Indian scholars). Although few in number, Hellenistic mathematicians actively communicated with each other; publication consisted of passing and copying someone's work among colleagues.
Later mathematicians include Diophantus (c. 214–298 AD), who wrote on polygonal numbers and a work in pre-modern algebra (Arithmetica),Pappus of Alexandria (c. 290-350 AD), who compiled many important results in the Collection, and Theon of Alexandria (c. 335-405 AD) and his daughter Hypatia (c. 370–415 AD), who edited Ptolemy's Almagest and other works. Although none of these mathematicians, save Diophantus, had notable original works, they are distinguished for their commentaries and expositions. These commentaries have preserved valuable extracts from works which have perished, or historical allusions which, in the absence of original documents, are precious because of their rarity.
Most of the mathematical texts written in Greek survived through the copying of manuscripts over the centuries, though some fragments dating from antiquity have been found in Greece, Egypt, Asia Minor, Mesopotamia, and Sicily.
Ancient Greek mathematics was not limited to theoretical works but was also used in other activities, such as business transactions and in land mensuration, as evidenced by extant texts where computational procedures and practical considerations took more of a central role.
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. The two major sources are
Nevertheless, despite the lack of original manuscripts, the dates of Greek mathematics are more certain than the dates of surviving Babylonian or Egyptian sources because a large number of overlapping chronologies exist. Even so, many dates are uncertain; but the doubt is a matter of decades rather than centuries.
^Knorr, W. (1981). On the early history of axiomatics: The interaction of mathematics and philosophy in Greek Antiquity. Theory Change, Ancient Axiomatics, and Galileo's Methodology, Vol. 1: D. Reidel Publishing Co. pp. 145–186.CS1 maint: location (link)
^Kahn, C. H. (1991). Some remarks on the origins of Greek science and philosophy. Science and Philosophy in Classical Greece: Garland Publishing Inc. pp. 1–10.