Pierre de Fermat

Abstract

Throughout his lifetime, Pierre de Fermat was associated with the country in and about Toulouse. He studied law in the local university and later became a member of the local parliament. His leisure time was given over to the study of mathematics and he made contributions to most if not to all of the branches of mathematics then known. Fermat's discoveries were preserved in his Varia Opera Mathematica edited by his son Samuel de Fermat and published at Toulouse in 1679, in his notes to Bachet's translation of Diophantus which were also published by the younger Fermat in 1670, and in his correspondence vvith other mathematicians among whom were Roberval and Pascal. It is difficult, accordingly, to give the precise dates of Fermat's various discoveries, but it is probable that his work on maxima and minima was done by 1629. Professor Cajori says of this that “He substituted x + e for x in the given function of x and then equated to each other the successive values of the function and divided the equation by e. If e be taken 0, then the roots of this equation are the values of x, making the function a maximum or a minimum…. The main difference between it and the rule of the differential calculus is that it introduces the indefinite quantity e instead of the infinitely small dx.” This method was attacked by Descartes and the dispute that followed involved many of the important French mathematicians.