# Mathematician:Mathematicians/Sorted By Birth/BCE

For more comprehensive information on the lives and works of mathematicians through the ages, see the MacTutor History of Mathematics archive, created by John J. O'Connor and Edmund F. Robertson.

*The army of those who have made at least one definite contribution to mathematics as we know it soon becomes a mob as we look back over history; 6,000 or 8,000 names press forward for some word from us to preserve them from oblivion, and once the bolder leaders have been recognised it becomes largely a matter of arbitrary, illogical legislation to judge who of the clamouring multitude shall be permitted to survive and who be condemned to be forgotten.*- -- Eric Temple Bell:
*Men of Mathematics*, 1937, Victor Gollancz, London

- -- Eric Temple Bell:

## Contents

- 1 BCE $\text {2000}$ – $\text {1001}$
- 2 BCE $\text {1000}$ – $\text {701}$
- 3 BCE $\text {700}$ – $\text {601}$
- 4 BCE $\text {600}$ – $\text {501}$
- 5 BCE $\text {500}$ – $\text {401}$
- 5.1 Hippasus of Metapontum (5th century BCE )
- 5.2 Zeno of Elea (c. 490 – c. 430 BCE)
- 5.3 Oenopides of Chios (c. 490 – c. 420 BCE)
- 5.4 Hippocrates of Chios (c. 470 – 410 BCE)
- 5.5 Socrates (c. 469 – 399 BCE)
- 5.6 Theodorus of Cyrene (465 – 398 BCE)
- 5.7 Democritus (c. 460 – 370 BCE)
- 5.8 Hippias of Elis (c. 460 – c. 390 BCE)
- 5.9 Archytas of Tarentum (c. 428 – c. 350 BCE)
- 5.10 Plato (428/427 – 348/347 BCE)
- 5.11 Eudoxus of Cnidus (410 or 408 BCE – 355 or 347 BCE)

- 6 BCE $\text {400}$ – $\text {301}$
- 6.1 Xenocrates of Chalcedon (c. 396/5 – c. 314/3 BCE)
- 6.2 Dinostratus (c. 390 BCE – c. 320 BCE)
- 6.3 Aristotle (384 – 322 BCE)
- 6.4 Menaechmus (c. 380 BCE – c. 320 BCE)
- 6.5 Eudemus of Rhodes (c. 370 BCE – c. 300 BCE)
- 6.6 Aristaeus the Elder (c. 370 BCE – c. 300 BCE)
- 6.7 Autolycus of Pitane (c. 360 BCE – c. 290 BCE)
- 6.8 Diodorus Cronus (c. 350 – c. 284 BCE)
- 6.9 Aristarchus of Samos (310 – 230 BCE)

- 7 BCE $\text {300}$ – $\text {201}$
- 7.1 Euclid (c. 300 BCE )
- 7.2 Philo of Megara (c. 300 BCE )
- 7.3 Archimedes of Syracuse (c. 287 – 212 BCE)
- 7.4 Conon of Samos (c. 280 – c. 220 BCE)
- 7.5 Nicomedes (c. 280 – c. 210 BCE)
- 7.6 Eratosthenes of Cyrene (c. 276 – c. 195 BCE)
- 7.7 Apollonius of Perga (c. 262 – c. 190 BCE)
- 7.8 Dositheus of Pelusium (c. 250 BCE )
- 7.9 Diocles of Carystus (c. 240 – c. 180 BCE)
- 7.10 Pingala (c. 5th or 2nd century BCE )

- 8 BCE $\text {200}$ – $\text {101}$
- 9 BCE $\text {100}$ – $\text {1}$

## BCE $\text {2000}$ – $\text {1001}$

##### Ahmes (1681 BCE – 1621 BCE)

Egyptian scribe who wrote the *Rhind Papyrus*.
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## BCE $\text {1000}$ – $\text {701}$

##### Baudhayana (c. 800 BCE )

Indian mathematician, also a priest, believed to have flourished c. $800$ BCE.

Believed to have been a skilled craftsman, thus to have used his mathematical expertise in practical ways.

Did some early research into creating a circle with the same area as a given square.

Discovered $\pi$ to some degree of precision, and discovered what is now known as Pythagoras's Theorem.

Also evaluated the square root of 2 to five decimal places of accuracy.
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## BCE $\text {700}$ – $\text {601}$

##### Thales of Miletus (c. 625 – 547 BCE)

Greek mathematician, scientist, philosopher and astronomer, who (amongst other things) predicted a solar eclipse in 585 BCE.
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##### Anaximander of Miletus (611 – 546 BCE)

Greek philosopher who learned the teachings of his master Thales of Miletus.

Succeeded Thales as master, and may have taught Pythagoras.
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## BCE $\text {600}$ – $\text {501}$

##### Pythagoras of Samos (between 580 and 572 BCE – between 500 and 490 BCE)

Greek philosopher whose contributions to mathematics were perhaps more limited than is generally believed.

Best known for being said to have provided the first known proof of Pythagoras's Theorem (or one of his students did) which had probably been known to the ancient Egyptians.
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## BCE $\text {500}$ – $\text {401}$

##### Hippasus of Metapontum (5th century BCE )

Philosopher of the Pythagorean school.

Credited with the construction of the dodecahedron within the sphere.

Also sometimes credited with the discovery of irrational numbers.

Supposed to have drowned at sea, as a punishment for having revealed the existence of either irrational numbers, or the construction of the dodecahedron.

Supposedly founded the branch of the Pythagorean school known as the Mathematici.
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##### Zeno of Elea (c. 490 – c. 430 BCE)

Greek: **Ζήνων ὁ Ἐλεάτης**.

Pre-Socratic philosopher of southern Italy.

Member of the Eleatic School founded by Parmenides. Aristotle called him the "inventor of the dialectic".

Best known for his paradoxes, which Bertrand Russell described as "immeasurably subtle and profound".
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##### Oenopides of Chios (c. 490 – c. 420 BCE)

Mathematician, geometer and astronomer.

Little is known about him except that he came from the island of Chios, and is generally believed to have lived and worked in Athens in his youth.

Estimated the tilt of the Earth's axis with respect to the ecliptic as $24^\circ$.

May have introduced the rule that all geometric constructions must be done with a straightedge and compass.
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##### Hippocrates of Chios (c. 470 – 410 BCE)

Mathematician, geometer and astronomer.

The first to write a systematic textbook on geometry, *Elements of Geometry*, only a fragment of which survives.

Invented the technique of reduction, that is, transforming a mathematical problem into a more general, easily solvable one.

Demonstrated that the problem of Doubling the Cube is equivalent to finding the Cube Root of 2.

The first geometer to work out the area of a curvilinear figure (that is, the Lune of Hippocrates).

May have been a pupil of Oenopides of Chios.
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##### Socrates (c. 469 – 399 BCE)

**Socrates** (Greek: Σωκράτης, Sōkrátēs) was a Greek philosopher, a teacher of Plato.

Although no writings of his survive (if there ever were any), much of his philosophy has been documented in the works of Plato.

Executed by hemlock in $399$ BCE supposedly for the crime of corrupting the young.
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##### Theodorus of Cyrene (465 – 398 BCE)

Ancient Libyan Greek mathematician best known for the mathematical theorem now known as the Spiral of Theodorus.

Taught mathematics to Plato.

Proved that the square roots of the natural numbers from $3$ to $17$, except for $4$, $9$ and $16$, are irrational.
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##### Democritus (c. 460 – 370 BCE)

**Democritus** (Greek: **Δημόκριτος**, **Dēmokritos**, **chosen of the people**) was a Greek mathematician and philosopher, most famous for his atomic theory of the universe.

Also cited by Archimedes as having discovered the formula for the volume of a cone as being one third the volume of a cylinder of the same base and height, and the similar formula for the volume of a pyramid.
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##### Hippias of Elis (c. 460 – c. 390 BCE)

Greek sophist who lectured on poetry, grammar, history, politics, mathematics, and much else.
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##### Archytas of Tarentum (c. 428 – c. 350 BCE)

Greek philosopher, mathematician, astronomer, statesman, and strategist.

He was a scientist of the Pythagorean school.

Reputedly the founder of mathematical mechanics.
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##### Plato (428/427 – 348/347 BCE)

**Plato** (Greek: **Πλάτων**, Plátōn, "broad") was a Greek philosopher, a student and friend of Socrates and teacher of Aristotle.

Importantly documents the philosophy of Socrates.

Of particular importance was his insistence on the idea of proof.

Founded an academy.
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##### Eudoxus of Cnidus (410 or 408 BCE – 355 or 347 BCE)

Greek astronomer and mathematician.

Pioneered work on proportion.

Introduced the astronomical globe.

Developed the method of exhaustion, this being an early precursor to integral calculus. This was later exploited by Archimedes.

Studied and practised medicine, and was also a practising legislator.
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## BCE $\text {400}$ – $\text {301}$

##### Xenocrates of Chalcedon (c. 396/5 – c. 314/3 BCE)

Greek philosopher and mathematician born in what is now Turkey.

Leader of Plato's Academy between 339/8 and 314/3 BCE.
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##### Dinostratus (c. 390 BCE – c. 320 BCE)

Dinostratus (Greek: **Δεινόστρατος**) was a Greek mathematician and geometer

Known for using a quadratrix, specifically the Trisectrix of Hippias, to solve the problem of Squaring the Circle.
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##### Aristotle (384 – 322 BCE)

**Aristotle** (Greek: **Ἀριστοτέλης**, Aristotélēs) was a Greek philosopher, a student of Plato and teacher of Alexander the Great.

Frequently cited as having been the inventor of the field of study known as (classical) logic.

Phenomenally influential philosopher whose works (for better or for worse) shaped the entirety of the intellectual development of the Western world for over a millennium.

Most important from the point of view of mathematics for formulating the Principle of Non-Contradiction and the Law of the Excluded Middle.
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##### Menaechmus (c. 380 BCE – c. 320 BCE)

Greek mathematician and geometer.

Known for his friendship with Plato.

Apparently discovered conic sections, and used them to provide a solution to the problem of Doubling the Cube using the parabola and hyperbola.
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##### Eudemus of Rhodes (c. 370 BCE – c. 300 BCE)

Ancient Greek philosopher, considered the first historian of science.

A pupil of Aristotle, who edited and interpreted his teacher's work so as to make it more easily accessible.
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##### Aristaeus the Elder (c. 370 BCE – c. 300 BCE)

Differentiated by Pappus of Alexandria from another later Aristaeus whose existence is no longer recorded.

Did considerable work on conic sections, but this was rendered obsolete by subsequent work by Apollonius.

Proved that "the same circle circumscribes both the pentagon of the dodecahedron and the triangle of the icosahedron inscribed in the same sphere."
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##### Autolycus of Pitane (c. 360 BCE – c. 290 BCE)

Greek astronomer, mathematician and geographer.
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##### Diodorus Cronus (c. 350 – c. 284 BCE)

Greek philosopher who propagated the interpretation of the conditional statement as a formal implication, as opposed to the more inclusive Rule of Material Implication.
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##### Aristarchus of Samos (310 – 230 BCE)

Greek astronomer and mathematician who used parallax to determine the relative distances of the moon and the sun.

His result was inaccurate, based as it was on faulty input data, but the method was sound.

One of the first to suggest a heliocentric universe.
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## BCE $\text {300}$ – $\text {201}$

##### Euclid (c. 300 BCE )

Greek mathematician about whom little is known, apart from:

- He taught in Alexandria (then a Macedonian colony, the hub of the Hellenic world);
- He assembled the geometry text
*The Elements*, possibly the most famous mathematics text book of all time.

##### Philo of Megara (c. 300 BCE )

Greek philosopher who worked on establishing the Rule of Material Implication, differentiating it from formal implication.

A pupil of Diodorus Cronus, who favoured the interpretation of formal implication.
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##### Archimedes of Syracuse (c. 287 – 212 BCE)

Greek mathematician, physicist, astronomer, engineer and general all-round inventor.

Perfected the method of exhaustion.
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##### Conon of Samos (c. 280 – c. 220 BCE)

Greek astronomer and mathematician.

Noted for naming the constellation Coma Berenices.

According to Pappus, the discoverer of the spiral of Archimedes.

According to Apollonius of Perga, Conon worked on conic sections, and his work became the basis for Apollonius' fourth volume of the *Conics*.
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##### Nicomedes (c. 280 – c. 210 BCE)

Ancient Greek mathematician about whom almost nothing is known.

Creator of the curve now known as the Conchoid of Nicomedes, which he used for Doubling the Cube.
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##### Eratosthenes of Cyrene (c. 276 – c. 195 BCE)

Greek geometer and astronomer best known for his estimate of the size of the Earth.

Also famous for his Sieve of Eratosthenes.
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##### Apollonius of Perga (c. 262 – c. 190 BCE)

Ancient Greek: **Ἀπολλώνιος**, also known (in the Latin form) as **Pergaeus**.

Greek geometer and astronomer best known for his work on conic sections, in which he uses techniques in analytic geometry which anticipated the work of Descartes.

Greatly influential, he provided the names of the ellipse, parabola and hyperbola.
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##### Dositheus of Pelusium (c. 250 BCE )

Greek astromnomer and mathematician who was a friend or pupil of Conon of Samos.

On the death of Conon, Archimedes of Syracuse chose Dositheus to be the recipient of several treatises, including *On the Quadrature of the Parabola*, *On Spirals*, *On the Sphere and Cylinder* (two books), and *On Conoids and Spheroids*.
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##### Diocles of Carystus (c. 240 – c. 180 BCE)

Greek mathematician and geometer, thought to be the first person to prove the focal property of the parabola.

Also associated with the Cissoid of Diocles, which was used by Diocles to solve the problem of Doubling the Cube.
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##### Pingala (c. 5th or 2nd century BCE )

Indian mathematician about whom practically nothing is known, not even when he lived.

Notable for being the first in history to mention what is now known as Pascal's Triangle.
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## BCE $\text {200}$ – $\text {101}$

##### Hypsicles of Alexandria (c. 190 – c. 120 BCE)

Alexandrian mathematician and astronomer best known for having Book $\text{XIV}$ of Euclid's *The Elements* attributed to him.

Whether or not he was also responsible for Book $\text{XV}$ of *The Elements* is still up for debate.

Also appears to have written a (now lost) work on polygonal numbers.
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##### Hipparchus of Nicaea (c. 190 – c. 120 BCE)

Greek astronomer, geographer, and mathematician of Turkish origin.

Derived the first known set of trigonometrical tables.

Discovered the precession of the equinoxes.
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##### Theodosius of Bithynia (c. 160 – c. 100 BCE)

Greek astronomer and mathematician best known for writing *Sphaerics*, a book on spherical geometry.

According to Vitruvius, he is supposed to have invented a sundial which would work anywhere in the world.

Sometimes confused with various other writers called Theodosius. On this basis, often erroneously believed to have been born in Tripolis.
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##### Perseus (c. 150 BCE )

Greek geometer, who invented the concept of spiric sections.

Only $2$ references to him exist, and both are in the writings of Proclus Lycaeus.
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##### Posidonius (c. 135 – c. 51 BCE)

Greek Stoic philosopher, politician, astronomer, geographer, historian and teacher.

Acclaimed as the greatest polymath of his age.

One of the first to attempt to prove Euclid's fifth postulate.
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## BCE $\text {100}$ – $\text {1}$

##### Geminus of Rhodes (c. 10 BCE – c. 60 CE)

Greek astronomer and mathematician about whom practically nothing is known.

Named the cissoid of Diocles after Diocles of Carystus.

Gave a proof (incorrect) of Euclid's fifth postulate, the first on record.
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