# Timeline of ancient Greek mathematicians

__: Timeline and summary of ancient Greek mathematicians and their discoveries__

**Short description**

This is a **timeline of mathematicians in Ancient Greece **.

## 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

<timeline>
DateFormat=yyyy ImageSize = width:830 height:auto barincrement:23 Period = from:-700 till:600 TimeAxis = orientation:horizontal AlignBars = justify PlotArea = width:700 top:0 left:100 bottom:30 Colors = id:line value:rgb(0.8,0.6,0.8) id:liteline value:rgb(0.3,0.9,0.9) id:bg value:white id:color360 value:rgb(0.3,0.6,0.0) id:color363 value:rgb(0.3,0.6,0.3) id:color366 value:rgb(0.3,0.6,0.6) id:color369 value:rgb(0.3,0.6,0.9) id:color390 value:rgb(0.3,0.9,0.0) id:color393 value:rgb(0.3,0.9,0.3) id:color396 value:rgb(0.3,0.9,0.6) id:color399 value:rgb(0.3,0.9,0.9) id:color660 value:rgb(0.6,0.6,0.0) id:color663 value:rgb(0.6,0.6,0.3) id:color666 value:rgb(0.6,0.6,0.6) id:color669 value:rgb(0.6,0.6,0.9) id:color690 value:rgb(0.6,0.9,0.0) id:color693 value:rgb(0.6,0.9,0.3) id:color696 value:rgb(0.6,0.9,0.6) id:color699 value:rgb(0.6,0.9,0.9) id:color900 value:rgb(0.9,0.0,0.0) id:color903 value:rgb(0.9,0.0,0.3) id:color906 value:rgb(0.9,0.0,0.6) id:color909 value:rgb(0.9,0.0,0.9) id:color930 value:rgb(0.9,0.3,0.0) id:color933 value:rgb(0.9,0.3,0.3) id:color936 value:rgb(0.9,0.3,0.6) id:color939 value:rgb(0.9,0.3,0.9) id:color960 value:rgb(0.9,0.6,0.0) id:color963 value:rgb(0.9,0.6,0.3) id:color966 value:rgb(0.9,0.6,0.6) id:color969 value:rgb(0.9,0.6,0.9) id:color990 value:rgb(0.9,0.9,0.0) id:color993 value:rgb(0.9,0.9,0.3) id:color996 value:rgb(0.9,0.9,0.6) ScaleMajor = gridcolor:line unit:year increment:100 start:-700 ScaleMinor = gridcolor:liteline unit:year increment:20 start:-700 PlotData= fontsize:M width:15 textcolor:black align:center shift:(0,-4) 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" bar:Hypsicles from:-190 till:-120 color:color996 text:"Hypsicles" bar:Perseus from:-180 till:-120 color:color360 text:"Perseus" bar:Theodosius from:-169 till:-100 color:color363 text:"Theodosius" 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" bar:Cleomedes from:10 till:70 color:color396 text:"Cleomedes" bar:Heron from:10 till:70 color:color660 text:"Heron" bar:Nicomachus from:60 till:120 color:color399 text:"Nicomachus" bar:Menelaus from:70 till:140 color:color666 text:"Menelaus" bar:Theon_of_Smyrna from:70 till:135 color:color663 text:"Theon of Smyrna" bar:Ptolemy from:100 till:170 color:color390 text:"Ptolemy" bar:Diophantus from:207 till:291 color:yellow text:"Diophantus" bar:Porphyry from:234 till:305 color:color363 text:"Porphyry" bar:Sporus from:240 till:300 color:color969 text:"Sporus of Nicaea" bar:Pappus from:290 till:350 color:color369 text:"Pappus" bar:Serenus from:300 till:360 color:color696 text:"Serenus" bar:Theon2 from:335 till:405 color:color930 text:"Theon" bar:Hypatia from:360 till:415 color:color663 text:"Hypatia" bar:Proclus from:412 till:485 color:color933 text:"Proclus" 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" bar:Eutocius from:480 till:540 color:color969 text:"Eutocius" bar:Simplicius from:490 till:560 color:color690 text:"Simplicius" LineData = at:-600 color:green at:-300 color:orange at:0 color:black at:300 color:red </timeline> |

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

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 [math]\displaystyle{ 5 \cdot 5 }[/math] for example, would often be constructed as a literal square with sides of length [math]\displaystyle{ 5, }[/math] which is why the second power "[math]\displaystyle{ x^2 = x \cdot x }[/math]" is referred to as "[math]\displaystyle{ x }[/math] 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 – Study of how mathematics and physics relate to each other
- 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

- ↑ (Boyer 1991)
- ↑ Weyl 1952, p. 74.
- ↑ Calinger, Ronald (1982).
*Classics of Mathematics*. Oak Park, Illinois: Moore Publishing Company, Inc.. p. 75. ISBN 0-935610-13-8. - ↑ 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. - ↑ 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. - ↑ 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." - ↑ 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" - ↑ "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.
- ↑ 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.

Original source: https://en.wikipedia.org/wiki/Timeline of ancient Greek mathematicians.
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