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Euclid was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers, or defined as generalizations of the integers.
Proclus Lycius, called Proclus the Successor, was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, Early Islamic philosophy, Scholastic philosophy, and German Idealism, especially G.W.F. Hegel, who called Proclus's Platonic Theology "the true turning point or transition from ancient to modern times, from ancient philosophy to Christianity."
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia.
Pappus of Alexandria was a Greek mathematician of late antiquity known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a mathematics teacher to higher level students, one of whom was named Hermodorus.
Nicomachus of Gerasa was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria. Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works Introduction to Arithmetic and Manual of Harmonics, which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in Late antiquity, with philosophers such as Iamblichus and John Philoponus writing commentaries on it. A Latin paraphrase by Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education.
Iamblichus was a Syrian neoplatonic philosopher. He determined a direction later taken by neoplatonism. Iamblichus was also the biographer of the Greek mystic, philosopher, and mathematician Pythagoras. In addition to his philosophical contributions, his Protrepticus is important for the study of the sophists because it preserved about ten pages of an otherwise unknown sophist known as the Anonymus Iamblichi.
Hippasus of Metapontum was a Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this and crediting it to himself instead of Pythagoras which was the norm in Pythagorean society. However, the few ancient sources who describe this story either do not mention Hippasus by name or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer.
Thomas Taylor was an English translator and Neoplatonist, the first to translate into English the complete works of Aristotle and of Plato, as well as the Orphic fragments.
Theodorus of Cyrene was an ancient Greek mathematician. The only first-hand accounts of him that survive are in three of Plato's dialogues: the Theaetetus, the Sophist, and the Statesman. In the former dialogue, he posits a mathematical construction now known as the Spiral of Theodorus.
Syrianus was a Greek Neoplatonist philosopher, and head of Plato's Academy in Athens, succeeding his teacher Plutarch of Athens in 431/432 A.D. He is important as the teacher of Proclus, and, like Plutarch and Proclus, as a commentator on Plato and Aristotle. His best-known extant work is a commentary on the Metaphysics of Aristotle. He is said to have written also on the De Caelo and the De Interpretatione of Aristotle and on Plato's Timaeus.
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century BC to the 6th century AD, around the shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire region, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.
Geminus of Rhodes, was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the Introduction to the Phenomena, still survives; it was intended as an introductory astronomy book for students. He also wrote a work on mathematics, of which only fragments quoted by later authors survive.
Theon of Smyrna was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. His surviving On Mathematics Useful for the Understanding of Plato is an introductory survey of Greek mathematics.
The Academy, variously known as Plato's Academy, the Platonic Academy, and the Academic School, was founded at Athens by Plato circa 387 BC. Aristotle studied there for twenty years before founding his own school, the Lyceum. The Academy persisted throughout the Hellenistic period as a skeptical school, until coming to an end after the death of Philo of Larissa in 83 BC. The Platonic Academy was destroyed by the Roman dictator Sulla in 86 BC.
Hypsicles was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and possibly the Book XIV of Euclid's Elements. Hypsicles lived in Alexandria.
This page is a list of topics in ancient philosophy.
Commentaries on Plato refers to the great mass of literature produced, especially in the ancient and medieval world, to explain and clarify the works of Plato. Many Platonist philosophers in the centuries following Plato sought to clarify and summarise his thoughts, but it was during the Roman era, that the Neoplatonists, in particular, wrote many commentaries on individual dialogues of Plato, many of which survive to the present day.
Many interpreters of Plato held that his writings contain passages with double meanings, called allegories, symbols, or myths, that give the dialogues layers of figurative meaning in addition to their usual literal meaning. These allegorical interpretations of Plato were dominant for more than fifteen hundred years, from about the 1st century CE through the Renaissance and into the 18th century, and were advocated by major Platonist philosophers such as Plotinus, Porphyry, Syrianus, Proclus, and Marsilio Ficino. Beginning with Philo of Alexandria, these views influenced the Jewish, Christian, and Islamic interpretation of these religions' respective sacred scriptures. They spread widely during the Renaissance and contributed to the fashion for allegory among poets such as Dante Alighieri, Edmund Spenser, and William Shakespeare.
A History of Greek Mathematics is a book by English historian of mathematics Thomas Heath about history of Greek mathematics. It was published in Oxford in 1921, in two volumes titled Volume I, From Thales to Euclid and Volume II, From Aristarchus to Diophantus. It got positive reviews and is still used today. Ten years later, in 1931, Heath published A Manual of Greek Mathematics, a concise version of the two-volume History.
References
- Heath, Thomas Little (1981). A History of Greek Mathematics, Volume II. Dover publications. ISBN 0-486-24074-6.
- Ivor Bulmer-Thomas, Biography in Dictionary of Scientific Biography (New York 1970–1990).
- Peter Brown, The Manual of Domninus in Harvard Review of Philosophy (2000)
