Timeline of ancient Greek mathematicians

Short description: Timeline and summary of ancient Greek mathematicians and their discoveries

This is a timeline of mathematicians in Ancient Greece .

## Contents

* 1 Timeline
* 2 Overview of the most important mathematicians and discoveries
* 2.1 Hellenic mathematicians
* 3 Straightedge and compass constructions
* 3.1 Algebra
* 4 See also
* 5 References

## Timeline

Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus (ca. 624–548 BC), which is indicated by the green line at 600 BC. The orange line at 300 BC indicates the approximate year in which Euclid's Elements was first published. The red line at 300 AD passes through Pappus of Alexandria (c. 290 – c. 350 AD), who was one of the last great Greek mathematicians of late antiquity. Note that the solid thick black line is at year zero, which is a year that does not exist in the Anno Domini (AD) calendar year system

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bar:Thales                  from:-624 till:-548 color:yellow        text:"Thales of Miletus"
bar:Pythagoras              from:-570 till:-495 color:yellow        text:"Pythagoras"
bar:Hippasus                from:-530 till:-450 color:color669      text:"Hippasus"
bar:Anaxagoras              from:-500 till:-428 color:pink          text:"Anaxagoras"
bar:Zeno                    from:-495 till:-430 color:color363      text:"Zeno"
bar:Oenopides               from:-490 till:-420 color:color369      text:"Oenopides"
bar:Hippocrates             from:-470 till:-410 color:orange        text:"Hippocrates"
bar:Theodorus               from:-465 till:-398 color:color360      text:"Theodorus"
bar:Hippias                 from:-460 till:-400 color:color366      text:"Hippias"
bar:Democritus              from:-460 till:-370 color:color963      text:"Democritus"
bar:Bryson                  from:-450 till:-390 color:color390      text:"Bryson"
bar:Archytas                from:-428 till:-347 color:drabgreen     text:"Archytas"
bar:Theaetetus              from:-417 till:-369 color:color393      text:"Theaetetus"
bar:Thymaridas              from:-400 till:-350 color:color696      text:"Thymaridas"

bar:Eudoxus                 from:-408 till:-355 color:yellow        text:"Eudoxus"
bar:Xenocrates              from:-396 till:-314 color:color666      text:"Xenocrates"
bar:Dinostratus             from:-390 till:-320 color:color663      text:"Dinostratus"
bar:Menaechmus              from:-380 till:-320 color:color660      text:"Menaechmus"
bar:Aristaeus               from:-370 till:-300 color:color669      text:"Aristaeus the Elder"
bar:Callippus               from:-370 till:-300 color:color363      text:"Callippus"
bar:Autolycus               from:-360 till:-290 color:color669      text:"Autolycus"

bar:Euclid                  from:-325 till:-265 color:yellow        text:"Euclid"
bar:Aristarchus             from:-310 till:-230 color:color930      text:"Aristarchus"
bar:Archimedes              from:-287 till:-212 color:yellow        text:"Archimedes"

bar:Chrysippus              from:-279 till:-206 color:color933      text:"Chrysippus"
bar:Conon                   from:-280 till:-220 color:color963      text:"Conon"
bar:Philon                  from:-280 till:-220 color:color660      text:"Philon"
bar:Eratosthenes            from:-276 till:-194 color:color960      text:"Eratosthenes"

bar:Apollonius              from:-262 till:-190 color:yellow        text:"Apollonius"
bar:Dionysodorus            from:-250 till:-190 color:color969      text:"Dionysodorus"
bar:Diocles                 from:-240 till:-180 color:color369      text:"Diocles"
bar:Zenodorus               from:-200 till:-140 color:color963      text:"Zenodorus"
bar:Hipparchus              from:-190 till:-120 color:color696      text:"Hipparchus"
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bar:Perseus                 from:-180 till:-120 color:color360      text:"Perseus"
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bar:Zeno_of_Sidon           from:-150 till:-75  color:color366      text:"Zeno of Sidon"
bar:Posidonius              from:-135 till:-51  color:color393      text:"Posidonius"
bar:Geminus                 from:-100 till:-30  color:color669      text:"Geminus"

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bar:Domninus                from:420  till:480  color:color939      text:"Domninus"
bar:Marinus                 from:450  till:500  color:color960      text:"Marinus"
bar:Anthemius               from:474  till:535  color:color963      text:"Anthemius"
bar:Boethius                from:477  till:524  color:color393      text:"Boethius"
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The mathematician Heliodorus of Larissa is not listed due to the uncertainty of when he lived, which was possibly during the 3rd century AD, after Ptolemy.

## Overview of the most important mathematicians and discoveries

Of these mathematicians, those whose work stands out include:

* Thales of Miletus (c. 624/623 – c. 548/545 BC) is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales' theorem. He is the first known individual to whom a mathematical discovery has been attributed.[1]
* Pythagoras (c. 570 – c. 495 BC) was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus.
* Theaetetus (c. 417 – c. 369 BC) Proved that there are exactly five regular convex polyhedra (it is emphasized that it was, in particular, proved that there does not exist any regular convex polyhedra other than these five). This fact led these five solids, now called the Platonic solids, to play a prominent role in the philosophy of Plato (and consequently, also influenced later Western Philosophy) who associated each of the four classical elements with a regular solid: earth with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron (of the fifth Platonic solid, the dodecahedron, Plato obscurely remarked, "...the god used [it] for arranging the constellations on the whole heaven"). The last book (Book XIII) of the Euclid's Elements, which is probably derived from the work of Theaetetus, is devoted to constructing the Platonic solids and describing their properties; Andreas Speiser has advocated the view that the construction of the 5 regular solids is the chief goal of the deductive system canonized in the Elements.[2] Astronomer Johannes Kepler proposed a model of the Solar System in which the five solids were set inside one another and separated by a series of inscribed and circumscribed spheres.
* Eudoxus of Cnidus (c. 408 – c. 355 BC) is considered by some to be the greatest of classical Greek mathematicians, and in all Ancient Greece second only to Archimedes.[3] Book V of Euclid's Elements is though to be largely due to Eudoxus.
* Aristarchus of Samos (c. 310 – c. 230 BC) presented the first known heliocentric model that placed the Sun at the center of the known universe with the Earth revolving around it. Aristarchus identified the "central fire" with the Sun, and he put the other planets in their correct order of distance around the Sun.[4] In On the Sizes and Distances, he calculates the sizes of the Sun and Moon, as well as their distances from the Earth in terms of Earth's radius. However, Eratosthenes (c. 276 – c. 194/195 BC) was the first person to calculate the circumference of the Earth. Posidonius (c. 135 – c. 51 BC) also measured the diameters and distances of the Sun and the Moon as well as the Earth's diameter; his measurement of the diameter of the Sun was more accurate than Aristarchus', differing from the modern value by about half.
* Euclid (fl. 300 BC) is often referred to as the "founder of geometry"[5] or the "father of geometry" because of his incredibly influential treatise called the Elements, which was the first, or at least one of the first, axiomatized deductive systems.
* Archimedes (c. 287 – c. 212 BC) is considered to be the greatest mathematician of ancient history, and one of the greatest of all time.[6][7] Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral.[8] He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. In a lost work, he discovered and enumerated the 13 Archimedean solids, which were later rediscovered by Johannes Kepler around 1620 A.D.
* Apollonius of Perga (c. 240 – c. 190 BC) is known for his work on conic sections and his study of geometry in 3-dimensional space. He is considered one of the greatest ancient Greek mathematicians.
* Hipparchus (c. 190 – c. 120 BC) is considered the founder of trigonometry[9] and also solved several problems of spherical trigonometry. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. In his work On Sizes and Distances, he measured the apparent diameters of the Sun and Moon and their distances from Earth. He is also reputed to have measured the Earth's precession.
* Diophantus (c. 201–215 – c. 285–299 AD) wrote Arithmetica which dealt with solving algebraic equations and also introduced syncopated algebra, which was a precursor to modern symbolic algebra. Because of this, Diophantus is sometimes known as "the father of algebra," which is a title he shares with Muhammad ibn Musa al-Khwarizmi. In contrast to Diophantus, al-Khwarizmi wasn't primarily interested in integers and he gave an exhaustive and systematic description of solving quadratic equations and some higher order algebraic equations. However, al-Khwarizmi did not use symbolic or syncopated algebra but rather "rhetorical algebra" or ancient Greek "geometric algebra" (the ancient Greeks had expressed and solved some particular instances of algebraic equations in terms of geometric properties such as length and area but they did not solve such problems in general; only particular instances). An example of "geometric algebra" is: given a triangle (or rectangle, etc.) with a certain area and also given the length of some of its sides (or some other properties), find the length of the remaining side (and justify/prove the answer with geometry). Solving such a problem is often equivalent to finding the roots of a polynomial.

### Hellenic mathematicians

The conquests of Alexander the Great around c. 330 BC led to Greek culture being spread around much of the Mediterranean region, especially in Alexandria, Egypt. This is why the Hellenistic period of Greek mathematics is typically considered as beginning in the 4th century BC. During the Hellenistic period, many people living in those parts of the Mediterranean region subject to Greek influence ended up adopting the Greek language and sometimes also Greek culture. Consequently, some of the Greek mathematicians from this period may not have been "ethnically Greek" with respect to the modern Western notion of ethnicity, which is much more rigid than most other notions of ethnicity that existed in the Mediterranean region at the time. Ptolemy, for example, was said to have originated from Upper Egypt, which is far South of Alexandria, Egypt. Regardless, their contemporaries considered them Greek.

## Straightedge and compass constructions

Creating a regular hexagon with a straightedge and compass

For the most part, straightedge and compass constructions dominated ancient Greek mathematics and most theorems and results were stated and proved in terms of geometry. These proofs involved a straightedge (such as that formed by a taut rope), which was used to construct lines, and a compass, which was used to construct circles. The straightedge is an idealized ruler that can draw arbitrarily long lines but (unlike modern rulers) it has no markings on it. A compass can draw a circle starting from two given points: the center and a point on the circle. A taut rope can be used to physically construct both lines (since it forms a straightedge) and circles (by rotating the taut rope around a point).

Geometric constructions using lines and circles were also used outside of the Mediterranean region. The Shulba Sutras from the Vedic period of Indian mathematics, for instance, contains geometric instructions on how to physically construct a (quality) fire-altar by using a taut rope as a straightedge. These alters could have various shapes but for theological reasons, they were all required to have the same area. This consequently required a high precision construction along with (written) instructions on how to geometrically construct such alters with the tools that were most widely available throughout the Indian subcontinent (and elsewhere) at the time. Ancient Greek mathematicians went one step further by axiomatizing plane geometry in such a way that straightedge and compass constructions became mathematical proofs. Euclid's Elements was the culmination of this effort and for over two thousand years, even as late as the 19th century, it remained the "standard text" on mathematics throughout the Mediterranean region (including Europe and the Middle East), and later also in North and South America after European colonization.

### Algebra

Ancient Greek mathematicians are known to have solved specific instances of polynomial equations with the use of straightedge and compass constructions, which simultaneously gave a geometric proof of the solution's correctness. Once a construction was completed, the answer could be found by measuring the length of a certain line segment (or possibly some other quantity). A quantity multiplied by itself, such as 5⋅5 for example, would often be constructed as a literal square with sides of length 5, which is why the second power "x2=x⋅x" is referred to as "x squared" in ordinary spoken language. Thus problems that would today be considered "algebra problems" were also solved by ancient Greek mathematicians, although not in full generality. A complete guide to systematically solving low-order polynomials equations for an unknown quantity (instead of just specific instances of such problems) would not appear until The Compendious Book on Calculation by Completion and Balancing by Muhammad ibn Musa al-Khwarizmi, who used Greek geometry to "prove the correctness" of the solutions that were given in the treatise. However, this treatise was entirely rhetorical (meaning that everything, including numbers, was written using words structured in ordinary sentences) and did not have any "algebraic symbols" that are today associated with algebra problems – not even the syncopated algebra that appeared in Arithmetica.

## See also

* History of mathematics
* History of geometry - Historical development of geometry
* Geometry and topology
* Physics:Relationship between mathematics and physics - Relationship between fields of study
* Timeline of mathematics - None
* Timeline of algebra - Notable events in the history of algebra
* Timeline of calculus and mathematical analysis
* Timeline of geometry - Notable events in the history of geometry
* Timeline of mathematical logic - None

## References

1. ↑ (Boyer 1991)
2. ↑ Weyl 1952, p. 74.
3. ↑ Calinger, Ronald (1982). Classics of Mathematics. Oak Park, Illinois: Moore Publishing Company, Inc.. p. 75. ISBN 0-935610-13-8.
4. ↑ Draper, John William (2007). "History of the Conflict Between Religion and Science". in Joshi, S. T.. The Agnostic Reader. Prometheus. pp. 172–173. ISBN 978-1-59102-533-7.
5. ↑ Bruno, Leonard C. (2003). Math and Mathematicians: The History of Math Discoveries Around the World. Baker, Lawrence W.. Detroit, Mich.: U X L. pp. 125. ISBN 978-0-7876-3813-9. OCLC 41497065. https://archive.org/details/mathmathematicia00brun/page/125.
6. ↑ John M. Henshaw (10 September 2014). An Equation for Every Occasion: Fifty-Two Formulas and Why They Matter. JHU Press. p. 68. ISBN 978-1-4214-1492-8. https://books.google.com/books?id=-0ljBAAAQBAJ&pg=PA68. "Archimedes is on most lists of the greatest mathematicians of all time and is considered the greatest mathematician of antiquity."
7. ↑ Hans Niels Jahnke. A History of Analysis. American Mathematical Soc.. p. 21. ISBN 978-0-8218-9050-9. https://books.google.com/books?id=CVRZEXFVsZkC&pg=PA21. "Archimedes was the greatest mathematician of antiquity and one of the greatest of all times"
8. ↑ "A history of calculus". University of St Andrews. February 1996. Archived from the original on 15 July 2007. https://web.archive.org/web/20070715191704/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html.
9. ↑ C. M. Linton (2004). From Eudoxus to Einstein: a history of mathematical astronomy. Cambridge University Press. p. 52. ISBN 978-0-521-82750-8.

* Boyer, C.B. (1989), A History of Mathematics (2nd ed.), New York: Wiley, ISBN 978-0-471-09763-1 (1991 pbk ed. ISBN 0-471-54397-7)
* Weyl, Hermann (1952). Symmetry. Princeton, NJ: Princeton University Press. ISBN 0-691-02374-3. https://archive.org/details/symmetry0000weyl.

* v
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Ancient Greek mathematics

Mathematicians
(timeline)|

* Anaxagoras
* Anthemius
* Archytas
* Aristaeus the Elder
* Aristarchus
* Apollonius
* Archimedes
* Autolycus
* Bion
* Bryson
* Callippus
* Carpus
* Chrysippus
* Cleomedes
* Conon
* Ctesibius
* Democritus
* Dicaearchus
* Diocles
* Diophantus
* Dinostratus
* Dionysodorus
* Domninus
* Eratosthenes
* Eudemus
* Euclid
* Eudoxus
* Eutocius
* Geminus
* Heron
* Hipparchus
* Hippasus
* Hippias
* Hippocrates
* Hypatia
* Hypsicles
* Isidore of Miletus
* Leon
* Marinus
* Menaechmus
* Menelaus
* Metrodorus
* Nicomachus
* Nicomedes
* Nicoteles
* Oenopides
* Pappus
* Perseus
* Philolaus
* Philon
* Porphyry
* Posidonius
* Proclus
* Ptolemy
* Pythagoras
* Serenus
* Simplicius
* Sosigenes
* Sporus
* Thales
* Theaetetus
* Theano
* Theodorus
* Theodosius
* Theon of Alexandria
* Theon of Smyrna
* Thymaridas
* Xenocrates
* Zeno of Elea
* Zeno of Sidon
* Zenodorus

Treatises|

* Almagest
* Archimedes Palimpsest
* Arithmetica
* Conics (Apollonius)
* Elements (Euclid)
* On the Sizes and Distances (Aristarchus)
* On Sizes and Distances (Hipparchus)
* On the Moving Sphere (Autolycus)
* The Sand Reckoner

Problems|

* Problem of Apollonius
* Squaring the circle
* Doubling the cube
* Angle trisection

Centers|

* Cyrene
* Library of Alexandria
* Platonic Academy

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