Using our modern notation but the reasoning of Hypatia and

Diophantus, we let x be the number of measures of wine.

He emphasizes two sets of problems named after

Diophantus of Alexandria (fl.

The first instances of elliptic curves occur in the works of

Diophantus and Fermat.

A number of problems and their solutions are transcribed, diagrammed, and annotated in detail, and an appendix offers a resume of similar examples from the (non-general) solutions of the third-century

Diophantus of Alexandria.

The Fermat's doodle has also a hidden message - "I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain." - which Pierre de Fermat famously quoted in margin of his copy of the Arithmetica by

Diophantus of Alexandria in 1637.

Great arithmeticians and number theorists include

Diophantus of Mexandria, Pierre de Fermat, and Kurt Godel.

Such equations are called Diophantine equations in the honour of

Diophantus who studied them many centuries ago.

912) translated

Diophantus' Arithmetica as the Art of Algebra, he recast the Greek text's mathematical operations in terms of al-Khwarizmi's new discipline; this was a major conceptual shift that would not have been recognized by the Greeks, nor do we have any lexical justification for the translation the Greek word in that way.

Diophantus' claim to fame rests on his Arithmetica, in which he gives a treatment of indeterminate equations--usually two or more equations in several variables that have an infinite number of rational solutions.

Fermat's contribution became knownthrough a translation of

Diophantus Arithmetica by Claude Gaspard de Bachet (1591-1639) in 1621.

Derbyshire, a mathematician and linguist by education and systems analyst by profession, starts with the algebra of about 4,000 years ago and works up to

Diophantus, whose place as the father of algebra may be disputed but whose contributions nevertheless are universally admired, then through Hypatia, Cardano, Descartes, Newton, von Leibniz, Lagrange, Cauchy, Abel, Galois, Riemann, Lie, Poincare, Hilbert, NoetherLefschetz, Zariski, MacLane and Grothendieck, along with a host of other luminaries, giving readers accessible descriptions of their discoveries and even providing non-specialists with extra help on basics such as vector spaces, field theory and algebraic geometry.