He carried on a personal correspondence with Descartes, Toricelli, Pascal, Frenicle, Roberval, Huygens, and others, as well as with the great majority of the great geometers of England and Italy, but his closest friend was M de Carcavi, whom he met when they were colleagues at the Parliament of Toulouse. Carcavi, formerly Fermat's companion in study, now finds himself the heir of all his friend's papers.
But since the purpose of this journal is mainly to mak known through their works those who have become famous in the republic of letters, we shall content ourselves with giving a catalogue of the writings of this great man, and shall leave it to others to write fuller and more worthy tributes.
He excelled in all branches of mathematics, but particularly in number theory and in geometry. He invented a method of squaring parabolas of any degree.
He gave a method of maxima and minima which can be used not only for plane and for three-dimensional problems, but also enables one to find the tangents to curves and centres of gravity of solids, and to solve numerical problems.
He gave an introduction to loci, plane and three-dimensional, which is an analytical treatise on the solution of problems in two and three dimensions. This was written before M Descartes had published anything on the subject.
He wrote a treatise De contactibus sphaericis in which Fermat proved in three-dimensions theorems which M Viète, the Referendary, had only proved for plane figures.
He wrote another treatise in which he states and proves the propositions of Apollonius Pergaeus's two books on plane loci.
He gave a general method for finding the length of curved lines etc.
Moreover, he was very well acquainted with the Classics, and was often consulted in case of difficulty. He explained any number of obscure passages in ancient writings. Some of his notes on Athenaeus have recently been printed, and the tranlstor of Benedetto Castelli's work on measuring running water inserted into the work brilliant note of Fermat's on a letter of Synesius. The letter itself was so obscure that Père Petau, who wrote a commentary on Synesius, admitted that he could not understand it. Fermat also wrote many notes on Theon of Smyrna and other ancient authors. Most of these notes are to be found scattered among his letters because he did not often write on this sort of subject except in answer to requests from his friends.
His mathematical writings and his research into the Classics did not interfere with M de Fermat's devotion to his profession: indeed he carried out his duties so well that he passed for one of the best lawyers of his time.
But what is even more surprising is that despite having the strength of character inseparable from the rare qualities of mind which we have mentioned, he was also endowed with a sensibility which enabled him to write Latin, French and Spanish verse with as much elegance as if he had lived in the time of Augustus, or had passed his life at the Court of France or at the Court in Madrid. We shall present a more detailed discussion of this great man's work when we have collected together his published writings and have obtained his son's permission to publish the works which are still in manuscript.