Diophantus
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.
[3][4] Although not the earliest, the Arithmetica has the best-known use of algebraic notation to solve arithmetical problems coming from Greek antiquity.
[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.
Diophantus was born into a Greek family and is known to have lived in Alexandria, Egypt, during the Roman era, between AD 200 and 214 to 284 or 298.
[5][10][11][a] Much of our knowledge of the life of Diophantus is derived from a 5th-century Greek anthology of number games and puzzles created by Metrodorus.
Through art algebraic, the stone tells how old: 'God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son.
Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him.
Hermann Hankel, renowned German mathematician made the following remark regarding Diophantus:Our author (Diophantos) not the slightest trace of a general, comprehensive method is discernible; each problem calls for some special method which refuses to work even for the most closely related problems.
For this reason it is difficult for the modern scholar to solve the 101st problem even after having studied 100 of Diophantos's solutions.
Scholia on Diophantus by the Byzantine Greek scholar John Chortasmenos (1370–1437) are preserved together with a comprehensive commentary written by the earlier Greek scholar Maximos Planudes (1260 – 1305), who produced an edition of Diophantus within the library of the Chora Monastery in Byzantine Constantinople.
Fermat was not the first mathematician so moved to write in his own marginal notes to Diophantus; the Byzantine scholar John Chortasmenos (1370–1437) had written "Thy soul, Diophantus, be with Satan because of the difficulty of your other theorems and particularly of the present theorem" next to the same problem.
Diophantus himself refers to a work which consists of a collection of lemmas called The Porisms (or Porismata), but this book is entirely lost.
It has been studied recently by Wilbur Knorr, who suggested that the attribution to Hero is incorrect, and that the true author is Diophantus.
Editions of Arithmetica exerted a profound influence on the development of algebra in Europe in the late sixteenth and through the 17th and 18th centuries.
Diophantus considered negative or irrational square root solutions "useless", "meaningless", and even "absurd".
Mathematical historian Kurt Vogel states:[23]The symbolism that Diophantus introduced for the first time, and undoubtedly devised himself, provided a short and readily comprehensible means of expressing an equation...
In addition, even from the founding of Alexandria, small numbers of Egyptians were admitted to the privileged classes in the city to fulfill numerous civic roles.
