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

- Timeline
- Overview of the most important mathematicians and discoveries
- Hellenic mathematicians
- Straightedge and compass constructions
- Algebra
- See also
- References

History of Greece |
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Greeceportal |

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

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.

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 antiquity 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.

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.

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.

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 for example, would often be constructed as a literal square with sides of length which is why the second power "" is referred to as " 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 *.

- History of mathematics
- History of calculus – Aspect of history
- History of geometry – Historical development of geometry

- Geometry and topology
- Greek mathematics – Mathematics of Ancient Greeks
- Relationship between mathematics and physics – Study of how mathematics and physics relate to each other
- Timeline of mathematics
- Timeline of algebra – Notable events in the history of algebra
- Timeline of calculus and mathematical analysis – Summary of advancements in Calculus
- Timeline of geometry
- Timeline of mathematical logic

**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 new 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.

**Euclidean geometry** is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, *Elements*. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is *proved* from axioms and previously proved theorems.

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).

The **history of mathematics** deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.

In geometry, **straightedge-and-compass construction** – also known as **ruler-and-compass construction**, **Euclidean construction**, or **classical construction** – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.

**Squaring the circle** is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square.

The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. This article discounts mere speculation as discovery, although imperfect reasoned arguments, arguments based on elegance/simplicity, and numerically/experimentally verified conjectures qualify. The timeline begins at the Bronze Age, as it is difficult to give even estimates for the timing of events prior to this, such as of the discovery of counting, natural numbers and arithmetic.

**Greek mathematics** refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly attested from the late 7th 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 proofs is an important difference between Greek mathematics and those of preceding civilizations.

In mathematics, **quadrature** is a historical term for the process of determining area. This term is still used in the context of differential equations, where "solving an equation by quadrature" or "reduction to quadrature" means expressing its solution in terms of integrals.

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics and Indian mathematics. Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry.

In geometry, the **neusis** is a geometric construction method that was used in antiquity by Greek mathematicians.

The **history of mathematical notation** includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness. Mathematical notation comprises the symbols used to write mathematical equations and formulas. Notation generally implies a set of well-defined representations of quantities and symbols operators. The history includes Hindu–Arabic numerals, letters from the Roman, Greek, Hebrew, and German alphabets, and a host of symbols invented by mathematicians over the past several centuries.

Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.

**Algebra** is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics.

**Geometry** is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a *geometer*. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.

A timeline of **algebra** and **geometry**

A timeline of **calculus** and **mathematical analysis**.

This is a timeline of pure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm.

**Wilbur Richard Knorr** was an American historian of mathematics and a professor in the departments of philosophy and classics at Stanford University. He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century.

* The Ancient Tradition of Geometric Problems* is a book on ancient Greek mathematics, focusing on three problems now known to be impossible if one uses only the straightedge and compass constructions favored by the Greek mathematicians: squaring the circle, doubling the cube, and trisecting the angle. It was written by Wilbur Knorr (1945–1997), a historian of mathematics, and published in 1986 by Birkhäuser. Dover Publications reprinted it in 1993.

- ↑ ( Boyer 1991 , "Ionia and the Pythagoreans" p. 43)
- ↑ 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) [1874]. "History of the Conflict Between Religion and Science". In Joshi, S. T. (ed.).
*The Agnostic Reader*. Prometheus. pp. 172–173. ISBN 978-1-59102-533-7. - ↑ Bruno, Leonard C. (2003) [1999].
*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. - ↑ 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.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.Archimedes was the greatest mathematician of antiquity and one of the greatest of all times

- ↑ O'Connor, J.J.; Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews. Archived from the original on 15 July 2007. Retrieved 7 August 2007.
- ↑ 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.

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