Diophantus of Alexandria (; born probably sometime between AD 201 and 215; died aged 84, probably sometime between AD 285 and 299), sometimes called "the father of
algebra", was an
Alexandrian Greek mathematician and the author of a series of books called
Arithmetica, many of which are now lost. These texts deal with solving
algebraic equations. While reading
Claude Gaspard Bachet de Méziriac's edition of Diophantus'
Arithmetica, Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as
Fermat's Last Theorem. This led to tremendous advances in
number theory, and the study of
Diophantine equations ("Diophantine geometry") and of
Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. 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 the first
Greek mathematician who recognized fractions as numbers; thus he allowed
positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with
integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation.