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  • Topic: Diophantine equation, Fermat's Last Theorem, Pierre de Fermat
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Father of Algebra

Diophantus of Alexandria (Greek: Διόφαντος ὁ Ἀλεξανδρεύς) (c. 214 - c. 298 C.E.) was a Hellenistic mathematician. He is sometimes called "the Father of Algebra," a title he shares with Muhammad ibn Musa al-Khwarizmi. He is the author of a series of classical mathematical books called, The Arithmetica, and worked with equations which are now called Diophantine equations; the method to solve those problems is now called Diophantine analysis. The study of Diophantine equations is one of the central areas of number theory. Diophantus also authored a tract "On Polygonal Numbers" and a collection of propositions called Porisms. The findings and works of Diophantus have influenced mathematics greatly and caused many other questions to arise. The most famous of these is Fermat's Last Theorem. Diophantus also made advances in mathematical notation and was the first Hellenistic mathematician who frankly recognized fractions as numbers.

Biography

Little is known about the life of Diophantus. He lived in Alexandria, Egypt, probably from between 200 and 214 to 284 or 298 C.E. There is still a lot of speculation as to when he lived. According to Rafael Bombelli's Algebra, published in 1572, Diophantus lived under Antoninus Pius (138-161 C.E.), but there is no proof. Another source, a letter of Psellus (eleventh century), mentions Diophantus and Anatolius as writers on the Egyptian method of reckoning. It is taken, from that source, that Diophantus most probably flourished around 250 C.E. Most scholars consider Diophantus to have been a Greek,[1] though it has been suggested that he may have been a Hellenized Babylonian.[2] Almost everything known about Diophantus comes from a single fifth century Greek anthology, which is a collection of number games and strategy puzzles. One of the puzzles is: This tomb holds Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life. The translation and solution of this epigram-problem infers that Diophantus' boyhood lasted fourteen years, acquired a beard at 21, and married at age 33. He fathered a son five years later, but that son died at age 42—Diophantus, at this time, was 80 years old. He tried to distract himself from the grief with the science of numbers, and died 4 years later, at 84. This puzzle reveals that Diophantus lived to be about 84 years old. It is not certain if this puzzle is accurate or not.

Arithmetica

The Arithmetica is the major work of Diophantus and the most prominent work on algebra in Greek mathematics. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations. Of the original thirteen books of which Arithmetica consisted, only six have survived, though there are some who believe that four Arab books discovered in 1968 are also by Diophantus. Some Diophantine problems from Arithmetica have been found in Arabic sources.

History

After Diophantus's death, the Dark Ages began, spreading a shadow on math and science, and causing knowledge of Diophantus and the Arithmetica to be lost in Europe for roughly 1500 years. Sir Heath stated in his Diophantus of Alexandria, "After the loss of Egypt, the work of Diophantus long remained almost unknown among the Byzantines; perhaps one copy only survived (of the Hypatian recension), which was seen by Michael Psellus and possibly by the scholiast to Iamblichus, but of which no trace can be found after the capture of Constantinople in 1204." Possibly the only...
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