Pierre De Fermat Quotes

It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.

[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind. (Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)

It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain. [Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos & generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.]

Et peut-être la posterité me saura gré de lui avoir fait connaître que les Anciens n’ont pas tout su. (And perhaps, posterity will thank me for having shown that the ancients did not know everything.)

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.

The most famous Diophantine equation in history is the one known as Fermat's last Theorem, the celebrated statement by Pierre de Fermat (1601-55) that there are no whole number solutions to the equation x^n + y^n = z^n, where n is any number greater than 2. When n = 2, there are many solutions (in fact an infinite number). For instance, 3^2 + 4^2 = 5^2 (9 + 16 = 25); or 12^2 +5^2 = 13^2 (144 + 25 = 169). Miraculously, when we go from n = 2 to n = 3, there are no whole numbers x,y,z that satisfy x^3 + y^3 = z^3, and the same is true for any other value of n that is greater than 2. Appropriately, it was in the margin of the second book of Diophantus's Arithmetica, which Fermat was eagerly reading, that he wrote his extraordinary claim-one that took no fewer than 356 years to prove.

Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries. {In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.}

Cuius rei demostrationem mirabilem sane detexi hanc marginis exiquitas non caperet. Tengo una prueba verdaderamente maravillosa para esta afirmación, pero el margen es demasiado estrecho para contenerla.

Fermat’s Last Theorem dates to 1637. The French mathematician and physicist Pierre de Fermat had scribbled it in the margins of a book, adding that he had discovered a marvelous proof but that the margins were too small to hold it.