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Diophantus

For the general, see Diophantus (general). For the sophist, see Diophantus the Arab. For the intersex soldier, see Diophantus of Abae.

Diophantus of Alexandria[1] (born c. AD 200 – c. 214; died c. AD 284 – c. 298) was a Greek mathematician, who was the author of two main works: On Polygonal Numbers, which survives incomplete, and the Arithmetica in thirteen books, most of it extant, made up of arithmetical problems that are solved through algebraic equations.[2] He has been referred to as "the father of algebra".[3][4]

Although not the earliest, the Arithmetica has the best-known use of algebraic notation to solve arithmetical problems coming from Greek antiquity.[5][6] It was translated into Arabic in the 9th century AD and had some influence in the development of later algebra: Diophantus' method of solution matches medieval Arabic algebra in its concepts and overall procedure, and some problems from the Arithmetica have inspired modern work in both abstract algebra and number theory.[7][8]

Diophantus was among the first to recognized positive rational numbers as numbers, by allowing fractions for coefficients and solutions. He coined the term παρισότης (parisotēs) to refer to an approximate equality.[9] This term was rendered as adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves.

In modern use, Diophantine equations are algebraic equations with integer coefficients for which integer solutions are sought. Diophantine geometry and Diophantine approximations are two other subareas of number theory that are named after him.

  1. ^ Ancient Greek: Διόφαντος ὁ Ἀλεξανδρεύς, romanized: Diophantos ho Alexandreus
  2. ^ Carl B. Boyer, A History of Mathematics, Second Edition (Wiley, 1991), page 228
  3. ^ Derbyshire, John (2006). "The Father of Algebra". Unknown Quantity: A Real And Imaginary History of Algebra. Joseph Henry Press. pp. 31. ISBN 978-0-309-09657-7. Diophantus, the father of algebra, in whose honor I have named this chapter, lived in Alexandria, in Roman Egypt, in either the 1st, the 2nd, or the 3rd century CE.
  4. ^ Corry, Leo (2015). A Brief History of Numbers (1st ed.). Oxford University Press. p. 71. ISBN 978-0-19-870259-7. OCLC 907194512.
  5. ^ Research Machines plc. (2004). The Hutchinson dictionary of scientific biography. Abingdon, Oxon: Helicon Publishing. p. 312. Diophantus (lived c. A.D. 270-280) Greek mathematician who, in solving linear mathematical problems, developed an early form of algebra.
  6. '^ D. Mary, R. Flamary, C. Theys and C. Aime (2016). Mathematical Tools for Instrumentation & Signal Processing in Astronomy Volume 78-79, 2016. EAS Publications Series. pp. 73–98. Diophantus of Alexandria, a greek mathematician, known as the father of algebra. He studied polynomial equations with integer coefficients and integer solutions, called diophantine equations.{{cite book}}: CS1 maint: multiple names: authors list (link)
  7. ^ Hettle, Cyrus (2015). "The Symbolic and Mathematical Influence of Diophantus's Arithmetica". Journal of Humanistic Mathematics. 5 (1): 139–166. doi:10.5642/jhummath.201501.08.
  8. ^ Christianidis, Jean; Megremi, Athanasia (2019). "Tracing the early history of algebra: Testimonies on Diophantus in the Greek-speaking world (4th–7th century CE)". Historia Mathematica. 47: 16–38. doi:10.1016/j.hm.2019.02.002.
  9. ^ Katz, Mikhail G.; Schaps, David; Shnider, Steve (2013), "Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond", Perspectives on Science, 21 (3): 283–324, arXiv:1210.7750, Bibcode:2012arXiv1210.7750K, doi:10.1162/POSC_a_00101, S2CID 57569974
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