Diophantus

For the general, see Diophantus (general). For the sophist, see Diophantus the Arab.

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]

His Arithmetica influenced the development of algebra by Arabs, and his equations influenced modern work in both abstract algebra and computer science.[3] The first five books of his work are purely algebraic.[3] Furthermore, recent studies of Diophantus's work have revealed that the method of solution taught in his Arithmetica matches later medieval Arabic algebra in its concepts and overall procedure.[4]

Diophantus was the first Greek mathematician who 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.[5] 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.

Although not the earliest, the Arithmetica has the best-known use of algebraic notation to solve arithmetical problems coming from Greek antiquity,[6][2] and some of its problems served as inspiration for later mathematicians working in analysis and number theory.[7] 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. ^ a b Carl B. Boyer, A History of Mathematics, Second Edition (Wiley, 1991), page 228
  3. ^ a b 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.
  4. ^ 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.
  5. ^ 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
  6. ^ 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.
  7. '^ 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)