List of Ancient Mathematicians

Rhind: Encyclopaedia Britannica (also: Academic Edition, requires campus password)
Summary: Ancient Egyptian scroll bearing mathematical tables and problems. The source of much information about Egyptian mathematics. Bought in 1858 in a Nile resort town by a Scottish antiquary, Alexander Henry Rhind. Sometimes called the Ahmes papyrus in honour of the scribe who copied it about 1650 BC.

WIKI. Ahmes (more accurately Ahmose)
Summary: An Egyptian scribe. Lived during the Second Intermediate Period. Ahmes states that he copied the Rhind papyrus from a now-lost Middle Kingdom original, dating around 2000 BC. The 87 problems are presented with solutions, but often with no hint as to how the solution was obtained.

Thales (Θαλῆς ὁ Μιλήσιος)

MACTUTOR. Thales of Miletus
Born: about 624 BC in Miletus, Asia Minor (now Turkey)
Died: about 547 BC in Miletus, Asia Minor (now Turkey)
Summary: First known Greek philosopher, scientist and mathematician. Credited with five theorems of elementary geometry.

BRITANNICA. Thales of Miletus
flourished 6th century BC
Philosopher. Renowned as one of the legendary Seven Wise Men, or Sophoi. Remembered primarily for his cosmology: water as the essence of all matter, with the Earth a flat disk floating on a vast sea.

WIKI. Thales of Miletus also known as Thales the Milesian (Θαλῆς ὁ Μιλήσιος) (ca. 624 BC–ca. 546 BC)
Summary: Pre-Socratic Greek philosopher. One of the Seven Sages of Greece. Many regard him as the first philosopher in the Greek tradition as well as the father of science.

Internet Encyclopedia of Philosophy

Mactutor Pictures

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MACTUTOR. Pythagoras
Born: about 569 BC in Samos, Ionia
Died: about 475 BC
Summary: Philosopher. Made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.

BRITANNICA. Pythagoras
Born: c. 580 BC, Samos, Ionia
Died: c. 500, Metapontum, Lucania
Pythagoras, coloured woodcut from Theorica musicae by Gafurius, printed in Milan, 1492.
Summary: Greek philosopher, mathematician. Founder of the Pythagorean brotherhood that, although religious in nature, formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy.

WIKI. Pythagoras of Samos (Greek: Πυθαγόρας; circa 582 BC – circa 507 BC)
Summary: Ionic mathematician and philosopher. Founder of the mathematical, mystic, religious, and scientific society called Pythagoreans. Best known for the Pythagorean theorem which bears his name. Known as "the father of numbers". Made influential contributions to philosophy and religious teaching in the late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, one can say little with confidence about his life and teachings. He and his students believed that everything was related to mathematics and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles.

STANFORD. Pythagoras (ca. 570 to ca. 490 BC)
Summary: One of the most famous and controversial ancient Greek philosophers. Spent his early years on the island of Samos. At age forty: emigrated to the city of Croton in southern Italy and most of his philosophical activity occurred there. Wrote nothing. No detailed accounts of his thought written by contemporaries.

Internet Encyclopedia of Philosophy

The Complete Pythagoras. Contains a translation of ancient sources.

Wikipedia Pictures

The School of Athens, Raphael (1509)

Capitoline Museums, Rome

Vatican Museum

Looks like an ancient coin.

Pentagon

Mactutor and other Pictures

An ancient Greek coin, and a modern stamp.

Medallion from about 400 AD

From an edition of Boethius

Anaxagoras (Αναξαγόρας)

MACTUTOR. Anaxagoras of Clazomenae
Born: 499 BC in Clazomenae (30 km west of Izmir), Lydia (now Turkey)
Died: 428 BC in Lampsacus, Mysia (now Turkey)
Summary: Famed as the first to introduce philosophy to the Athenians. Imprisoned for claiming that the Sun was not a god and that the Moon reflected the Sun's light.

BRITANNICA. Anaxagoras
Born: c. 500 BC, Clazomenae, Anatolia [now in Turkey]
Died: c. 428, Lampsacus
Summary: Greek philosopher of nature. Remembered for his cosmology and for his discovery of the true cause of eclipses. Associated with the Athenian statesman Pericles.

WIKI. Anaxagoras (Greek: Αναξαγόρας, c. 500 BC–428 BC)
Summary: A pre-Socratic Greek philosopher. A member of what is now often called the Ionian School of philosophy.

Internet Encyclopedia of Philosophy

Empedocles

(Εμπεδοκλής)

MACTUTOR. NAME
Born: about 492 BC in Acragas (now Agrigento, Sicily,Italy)
Died: about 432 BC in Peloponnese, Greece
Summary: Greek philosopher. Best known for his belief that all matter was composed of four elements: fire, air, water, and earth. Some have considered him the inventor of rhetoric and the founder of the science of medicine in Italy.

BRITANNICA. Empedocles
Born: c. 490 BC, , Acragas, Sicily
Died: 430, the Peloponnese, Greece
Summary: Greek philosopher, statesman, poet, religious teacher, and physiologist. According to legend only, he was a self-styled god who brought about his own death by flinging himself into the volcanic crater atop Mount Etna to convince followers of his divinity. (Dramatized by the English poet Matthew Arnold in “Empedocles on Etna”)

WIKI. Empedocles (Greek: Εμπεδοκλής, circa 490 BCE – c. 430 BCE)
Summary: Greek presocratic philosopher. A citizen of Agrigentum, a Greek colony in Sicily. His philosophy best known for being the origin of the cosmogenic theory of the four classical elements. Little of the verse that he wrote survives today. Much of what is known about his philosophy comes from commentary upon it by later thinkers. His death has been the subject of both legend and a number of literary treatments.

STANFORD. Empedocles (ca. 495-435 BCE)
Summary: In antiquity, characterized as active on the democratic side in the politics of his native city of Acragas in Sicily, and as a physician, as well as a philosopher and poet. His philosophical and scientific theories are mentioned and discussed in several dialogues of Plato, and they figure prominently in Aristotle's writings on physics and biology and, as a result, also in the later Greek commentaries on Aristotle's works. His writings come down to us mostly in the form of fragments preserved as quotations in the works of these and other ancient authors. Extensive fragments, some of them not previously known, were recently found preserved on a papyrus roll from Egypt in the Strasbourg University library.

Internet Encyclopedia of Philosophy

Zeno of Elea

(Ζήνων ὁ Ἐλεάτης)

MACTUTOR. Zeno of Elea
Born: about 490 BC in Elea, Lucania (now southern Italy)
Died: about 425 BC in Elea, Lucania (now southern Italy)
Summary: Greek philosopher. Famous for paradoxes.

BRITANNICA. Zeno Of Elea
Born: c. 495 BC
Died: c. 430 BC
Summary: Greek philosopher and mathematician. Aristotle called the inventor of dialectic. Especially known for his paradoxes. Related to the Parmenidean doctrine of the existence of “the one” (i.e., indivisible reality). Sought to controvert the common-sense belief in the existence of “the many” (i.e., distinguishable qualities and things capable of motion). Son of a certain Teleutagoras and the pupil and friend of Parmenides. In Plato's Parmenides, Socrates, “then very young,” converses with Parmenides and Zeno, “a man of about forty”; but it may be doubted whether such a meeting was chronologically possible. Plato's account of Zeno's purpose (Parmenides), however, is presumably accurate. Zeno tried to show that the assumption of the existence of a plurality of things in time and space carried with it more serious inconsistencies. In early youth he collected his arguments in a book, which, according to Plato, was put into circulation without his knowledge.

WIKI. Zeno of Elea (IPA:zɛnoʊ, ɛlɛɑː, Greek: Ζήνων ὁ Ἐλεάτης) (circa 490 BC? – circa 430 BC?)
Summary: Pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Called by Aristotle the inventor of the dialectic. Best known for his paradoxes.

STANFORD. Zeno of Elea
Summary: Almost everything that we know about him is found in the opening pages of Plato's Parmenides. We learn that Zeno was nearly 40 years old when Socrates was a young man. We know is that he was close to Parmenides (Plato reports the gossip that they were lovers when Zeno was young), and that he wrote a book of paradoxes defending Parmenides' philosophy. This book has not survived. What we know of his arguments is second-hand, principally through Aristotle and his commentators. There were apparently 40 ‘paradoxes of plurality’, attempting to show that ontological pluralism leads to absurd conclusions. Only two definitely survive, probably a third. Aristotle speaks of a further four arguments against motion, all of which he gives and attempts to refute. In addition Aristotle attributes two other paradoxes to Zeno.

Internet Encyclopedia of Philosophy

Oenopides

MACTUTOR. Oenopides of Chios
Born: about 490 BC in Chios (now Khios), Greece
Died: about 420 BC
Summary: Made important contributions to astronomy. May have been the first to fix a value for the obliqity of the ecliptic.
DETAIL: Plato's Erastae: he acquired a reputation for mathematics. Plato also describes a scene where Socrates comes across two young men discussing a question in mathematical astronomy which had been tackled by Oenopides and Anaxagoras: seems to be the angle that the ecliptic. Probably proposed 24. Accepted in Greece until refined by Eratosthenes.
The period of the Great Year (combined cycle of sun and moon, but later the combined period of sun moon and planets): 59 years. Paul Tannery: this leads to a lunar month of 29.53013 days, the modern value is 29.53059 days. Many historians doubt whether Oenopides could have collected sufficient quality data for this (would requires 59 years). Paul Tannery: good for Saturn. It is only 2 from its starting position at the end of 59 years.
Proclus: he was responsible for two theorems in Euclid's Elements. (i) Draw perpendicular to a line from a given point not on the line. (ii) Construct on a line from a given point a line at a given angle to the first line. Heath believes that their significance might be that Oenopides set out for the first time the explicit 'ruler and compass' type of allowable construction.
Developed a theory to account for the Nile floods. Heat stored in the ground during the winter dries up the underground water so that the river shrinks. In the summer the heat disappears, as testing the temperature of deep wells suggests, and water flows up into the river so causing floods. This theory is false. It did not prove popular as other rivers in Libya were subject to similar conditions but did not behave in the same way.
Said to have believed in fire and air as basic elements. Thought of the world as a living being with God as its soul.

WIKI. Oenopides of Chios
Summary: Ancient Greek mathematician (geometer) and astronomer. Lived around 450 BCE. Born shortly after 500 BC on the island of Chios, but mostly worked in Athens
More detail:
Astronomy: Determined the angle between the plane of the celestial equator and the zodiac to be 24°, the standard value for two centuries, until Eratosthenes measured it with greater precision. Aso determined the value of the Great Year, that is, the shortest interval of time that is equal to both an integer number of years and an integer number of months. But the lunar orbit varies. He put the Great Year at 59 years (730 months). (in actuality 59 (sidereal) years are equal to 21550.1 days, while 730 (synodical) months equal 21557.3 days: the difference therefore amounts to seven days). Before him a Great Year of eight solar years was in use (= 99 months). Shortly after, in 432 BC, Meton and Euctemon discovered the better value of 18 years, equal to 223 months (the so-called Saros period).
In geometry: introduced the distinction between 'theorems' and 'problems': (a problem is only an isolated exercise without further follow-up or importance). Perhaps developed the rule that geometrical constructions should use only a compass and straightedge. Also two elementary constructions: (i) draw from a given point a straight line perpendicular to a given straight line; (ii) on a given straight line and at a given point on it, construct a rectilineal angle equal to a given rectilineal angle.
Said to have given an explanation of the flooding of the Nile each summer. On the basis of observations of the temperature of water in deep wells he seems erroneously to have inferred that underground water is in fact cooler in summer than in winter. In winter, when rain fell and seeped into the ground it would soon evaporate again because of the heat in the soil. However, in summer, when water in the ground was supposedly colder, there would be less evaporation. The surplus of moisture would then have to be carried off otherwise, thereby causing the Nile to overflow.
Attributed the opinion that formerly the sun had moved along the milky way. When it saw how Thyestes, a mythological figure, was served his own son for dinner by his brother Atreus, the sun was so horrified that it left its course and moved to the zodiac instead.
Said to have regarded the universe as a living organism, God or the Divine being its soul.
Said to have considered air and fire as being the first principles of the universe

Leucippus

(Λεύκιππος)

MACTUTOR. Leucippus of Miletus
Born: about 480 BC in (possibly) Miletus, Asia Minor
Died: about 420 BC
Summary: Greek philosopher. Originated the atomic theory of indivisibles developed later by Democritus.

Λεύκιππος

STANFORD. Leucippus
Summary: Greek tradition: Leucippus the founder of atomism in physics. Little is known about him. His views hard to distinguish from those of his associate Democritus. Sometimes said to have been a student of Zeno of Elea, devised the atomist philosophy in order to escape from the problems raised by Parmenides and his followers.

Internet Encyclopedia of Philosophy

Antiphon

MACTUTOR. Antiphon the Sophist
Born: 480 BC in (possibly) Athens, Greece
Died: 411 BC in Athens, Greece
Summary: Greek orator and statesman. Took up rhetoric as a profession. Was a Sophist and a contemporary of Socrates. (There is some dispute about whether there was one of two philosophers of this name). Made an early and important contribution to mathematics when he made an attempt to square the circle. In doing so he became the first to propose a method of exhaustion although it is not entirely clear how well he understood his own proposal. He proposed successively doubling the number of sides of a regular polygon inscribed in a circle so that the difference in areas would eventually become exhausted. There is dispute whether Antiphon was just being stupid or whether he had something subtle to say.

BRITANNICA. Antiphon
flourished c. 480—411 BC, Athens
Full Summary: orator and statesman. Earliest Athenian known to have taken up rhetoric as a profession. Writer of speeches for other men to deliver in their defense in court, a function that was particularly useful in the climate of accusation and counter-accusation that prevailed in Athens at the conclusion of the Peloponnesian War, between Athens and Sparta. Fifteen of his defenses (12 are exercises).
The prime mover in the anti-democratic revolution of the Four Hundred, an oligarchic council set up in 411 BC in an attempt to seize the Athenian government in the midst of war. Others may have been more conspicuous, but Thucydides' judgment in his History, is that it was Antiphon “who conceived the whole matter and the means by which it was brought to pass.” When the regime of the Four Hundred fell, he defended himself in a speech Thucydides describes as the greatest ever made by a man on trial for his life. Nevertheless, he was executed for treason.

WIKI. Antiphon the Sophist
Summary: Lived in Athens probably in the last two decades of the 5th century BC. There is an ongoing controversy over whether he is one and the same with Antiphon of the Athenian deme Rhamnus in Attica (480–411 BC), the earliest of the ten Attic orators.

Hippocrates of Chios

(Ἱπποκράτης)

MACTUTOR. Hippocrates of Chios
Born: about 470 BC in Chios (now Khios), Greece
Died: about 410 BC
Summary: Greek mathematician. Worked on the classical problems of squaring the circle and duplicating the cube.

BRITANNICA. Hippocrates of Chios
flourished c. 440 BC
Long summary: Greek geometer. Compiled the first known work on the elements of geometry. Euclid may have used it as a model for his Elements. No longer extant: known only through references by much later commentators, especially Proclus and Simplicius.

According to tradition, a merchant whose goods had been captured by pirates. Went to Athens to prosecute them but met with little success in recovering his property. Remained in Athens. Attended lectures on mathematics. Finally taught geometry to support himself.

Aristotle: different story. Cheated by customs officers in Byzantium. Moral: although a good geometer, incompetent in ordinary affairs.

In an attempt to square the circle, found areas of certain lunes. Summary of these quadratures, by Eudemus of Rhodes (c. 335 BC), with proofs, preserved by Simplicius. Proof uses a generalization of Pythagorean theorem involving semicircles instead of squares.

Duplicating the cubes reduces to finding two mean proportional. Possibly introduced the tactic of reducing a complex problem to a more tractable or simpler problem.

MACTUTOR. Theodorus of Cyrene
Born: 465 BC in Cyrene (now Shahhat, Libya)
Died: 398 BC in Cyrene (now Shahhat, Libya)
Summary: Greek philosopher (Cyrenaic school of moral philosophy). Pupil of Protagoras. Tutor of Plato and of Theaetetus.

WIKI. Theodorus of Cyrene (5th century BC)
Summary: Greek mathematician. Admired by Plato (References in Theatetus and other places). Plato: gave first proof of the irrationality of the square roots of 3 to 17. No useful insight as to the method is given. One popular conjecture involves a spiral comprised of contiguous right triangles with hypotenuse lengths equal to the square root of 2, square root of 3, square root of 4,..., up to the square root of 17 (where he stopped - possibly because additional triangles would cause the diagram to overlap). See Philip J. Davis, Spirals: From Theodorus to Chaos.

Hippias

(Ἱππίας)

Biography in Dictionary of Scientific Biography
Encyclopaedia Britannica (also: Academic Edition, requires campus password)

MACTUTOR. NAME
Born: about 460 BC in Elis, Peloponnese, Greece
Died: about 400 BC
Summary: Contemporary of Socrates. Developed the quadratrix - a curve he may have used for squaring the circle and trisecting angles.

BRITANNICA. Hippias Of Elis
flourished 5th century BC, Elis, in the Peloponnese, Greece
Full Summary: Sophist philosopher. Discovered the quadratrix. May have used it to trisect an angle. A man of great versatility, with an assurance characteristic of the later Sophists. Lectured on poetry, grammar, history, politics, archaeology, mathematics, and astronomy. Vast literary output: elegies and tragedies, and technical treatises in prose. Credited with an excellent work on Homer, collections of Greek and foreign literature, and archaeological treatises. Nothing remains except a few fragments. He is in Plato's Protagoras, and two of Plato's minor dialogues are named after him.

Biography in Dictionary of Scientific Biography
Encyclopaedia Britannica (also: Academic Edition, requires campus password)
Crater Democritus

MACTUTOR. Democritus of Abdera
Born: about 460 BC in Abdera, Thrace, Greece
Died: about 370 BC
Summary: Greek scholar. Best known for his atomic theory although he was also an excellent geometer.

BRITANNICA. Democritus
Born: c. 460 BC
Died: c. 370
Summary: Greek philosopher. Central figure in the development of the atomic theory of the universe.

STANFORD. Democritus
Summary: Known in antiquity as the ‘laughing philosopher’ because of his emphasis on the value of ‘cheerfulness'. One of the two founders of ancient atomist theory. Elaborated a system originated by his teacher Leucippus into a materialist account of the natural world.

Internet Encyclopedia of Philosophy

MACTUTOR. Bryson of Heraclea
Born: about 450 BC in Heraclea (now Taranto, Italy)
Died: unknown
Summary: Greek mathematician. Probably a pupil of Socrates. Contributed to the problem of squaring the circle. Themistius, an ancient commentator, writes that Bryson claimed that the circle was greater than all inscribed polygons and less than all circumscribed polygons. Improves Antiphon's argument. Bryson is getting close to the method of exhaustion.