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Timeline of ancient Greek mathematicians

## Summary

This is a timeline of ancient Greek mathematicians.

## 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) 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.

## Overview of the most important mathematicians and discoveries

Of these mathematicians, those whose work stands out include:

### 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 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. 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. Geometric constructions using a straightedge, such as that formed by a taut rope, and a compass 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 ${\displaystyle 5\cdot 5}$  for example, would often be constructed as a literal square with sides of length ${\displaystyle 5,}$  which is why the second power "${\displaystyle x^{2}=x\cdot x}$ " is referred to as "${\displaystyle x}$  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

## References

1. ^ (Boyer 1991, "Ionia and the Pythagoreans" p. 43)
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) [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.
5. ^ 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.
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. 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. Archimedes was the greatest mathematician of antiquity and one of the greatest of all times
8. ^ 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.
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.