FERMAT (PETER), an eminent French mathematician, who was born at Toulouse in 1590, and died in 1663. He was cotemporary with several mathematicians of the first order, among whom may be mentioned, Pascal, Des Cartes, Roberval, Torricelli, Huygens, Meziriac, Car cavi, Wallis, &c.; and furnished solutions of all the more difficult problems which these illustrious men were in the practice of proposing to one another. His predilection for numerical researches, led him to direct much of his atten tion to prime numbers, a subject which had been almost entirely neglected since the days of Erastosthenes. In these researches he afforded striking proofs of the superi ority of his genius, by the discovery of many general and curious properties of numbers which have no divisors, and such as are composite. The indeterminate analysis also occupied a good deal of his attention ; and though Bachet de Meziriac had already greatly extended and illustrated the Diophantine problems, his researches were far surpas sed, in elegance, simplicity and generalization, by those of Fermat. When Pascal was engaged at Paris in investiga ting the nature of figurate numbers, Fermat was eagerly prosecuting the same subject at Toulouse, by a different train of investigation ; and, indeed, on many occasions, these two great men were frequently led to the sameresults, by methods of enquiry which had little resemblance to each other. Such interferences in their pursuits, did not, how ever, weaken the friendship to which the conformity of their studies alone had given birth; and, though they were never personally acquainted, they uniformly did justice to the merits of each other, with a liberality which is unknown to little minds.
Fermat was scarcely more distinguished as a mathema tician than as a general scholar ; and, like most of the learned men who flourished in the age in which he lived, lie cultivated jurisprudence and elegant literature with no less assiduity and success, than geometry and algebra. The universality of his genius, and the extent of his attainments, procured the esteem of his fellow-citizens, and raised him to the dignity of a counsellor in the parliament of his native city.
But while we are disposed to admit the originality that characterizes the investigations of Fermat, we can not aquiesce in opinion with a modern writer of very high authority, we mean La Place,* who affirms, without any sort of proof, that he was the real inventor of the dif ferential calculus. The controversy on this subject has already been laid at rest ; and, as all the cotemporary wri ters were unanimous in ascribing the invention either to Newton or Leibnitz, the most unexceptionable evidence is now necessary, to support the claims of a third person to any share in the merit of the discovery. Fermat, indeed, in some of his investigations, employed methods resem bling the fluxionary calculus ; and the same thing had been done by Roberval and Pascal, in treating of the properties of the cycloid; but the circumstances which constitute a right to any important invention, must be founded, not upon obscure and indirect hints, but upon a distinct develope ment of its principles, and the actual application of these to the purposes of which they are susceptible of being ap plied. In this point of view, none of the predecessors of Newton or Leibnitz can come in competition with them ; and, without examining the merits of their respective claims, we must still consider them as dividing exclusive ly the honour of the greatest discovery that has ever been made by human ingenuity.
Fermat wrote dissertations on the following subjects : 1. A Method for the Quadrature of Parabolas ; 2. Another on Maxima and Minima; 3. An Introduction to Geometrical Loci; 4. A Treatise on Spherical Tangencies ; 5. A Resto ration of the two Books of Appolonius ou Plane Loci ; 6. A general Method for the Dimension of Curve Lines. His Opera varia Mathematica, printed at Toulouse in folio, 1679, contain also several smaller tracts, and a great num ber of letters to learned men. (A)