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Diophantus was a mathematician from Alexandria in ancient Greece. He lived sometime around 250 AD but giving exact dates is extremely difficult. No-one really knows for sure.

Diophantus was interested in solving polynomial equations with integer or rational equations. We now call these Diophantine equations.

The most famous Diophantine equation of them all is xn+yn=zn and Fermat's notorious marginal note

I have discovered a truly remarkable proof which this margin is too small to contain
was written in his copy of Diophantus' Arithmetica.

See also the proof of Diophantus' theorem on Pythagorean triples and Fermat's Last Theorem.

Diophantus of Alexandria, Greek algebraist, probably flourished about the middle of the 3rd century CE. Not that this date rests on positive evidence. But it seems a fair inference from a passage of Micael Psellus (Diophantus, ed. P. Tannery, ii. p. 38) that he was not later than Anatolius, bishop of Laodicea from 270 CE, while he is not quoted by Nicomachus (fl. c. 100 CE), nor by Theon of Smyrna (c. 130 CE) nor does Greek arithmetic as represented by these authors and by Iamblichus (end of 3rd century) show any trace of his influence, facts which can only be accounted for by his being later than those arithmeticians at least who would have been capable of understanding him fully. On the other hand he is quoted by Theon of Alexandria (who observed an eclipse at Alexandria in 365 CE); and his work was the subject of a commentary by Theon’s daughterHypatia (d. 415).

The Arithmetica, the greatest treatise on which the fame of Diophantus rests, purports to be in 13 books, but none of the Greek MS. which have survived contain more than six (though one has the same text in seven books). They contain, however, a fragment of a separate tract on Polygonal Numbers. The missing books were apparently lost early, for there is no reason to suppose that the Arabs who translated or commented on Diophantus ever had access to more of the work than we now have. The difference in form and content suggests that Polygonal Numbers was not part of the larger work. On the other hand the Porisms, to which Diophantus makes thre references ("we have it from the Porisms that…"), were probably not a separate work but were embodied in the Arithmetica itself, whether placed all together, or, as Tannery things, spread over the work in appropriate places. The "Porisms" quoted are interesting propositions in the theory of numbers, one of which was clearly that the difference between two cubes can be resolved into the sum of two cubes. Tannery thinks that he solution of a complete quadratic promised by Diophantus (I. def. II), and really assumed later, was one of the Porisms.

From the eleventh edition of The Encyclopedia, 1911. Public domain. Some editing has been done for the sake of clarity and for other reasons. If there is a problem with something, /msg me, rather that randomly downvoting.

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