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Pierre de Fermat
(17 Aug 1601 - 12 Jan 1665)

French mathematician who has been called the founder of the modern theory of numbers


Science Quotes by Pierre de Fermat (3 quotes)

Toutes les fois que dans une équation finale on trouve deux quantités inconnues, on a un lieu, l'extrémité de l'une d’elles décrivant une ligne droite ou courbe. La ligne droite est simple et unique dans son genre; les espèces des courbes sont en nombre indéfini, cercle, parabole, hyperbole, ellipse, etc.
Whenever two unknown magnitudes appear in a final equation, we have a locus, the extremity of one of the unknown magnitudes describing a straight line or a curve. The straight line is simple and unique; the classes of curves are indefinitely many,—circle, parabola, hyperbola, ellipse, etc.
— Pierre de Fermat
Introduction aux Lieux Plans et Solides (1679) collected in OEuvres de Fermat (1896), Vol. 3, 85. Introduction to Plane and Solid Loci, as translated by Joseph Seidlin in David E. Smith(ed.)A Source Book in Mathematics (1959), 389. Alternate translation using Google Translate: “Whenever in a final equation there are two unknown quantities, there is a locus, the end of one of them describing a straight line or curve. The line is simple and unique in its kind, species curves are indefinite in number,—circle, parabola, hyperbola, ellipse, etc.”
Science quotes on:  |  Circle (10)  |  Curve (9)  |  Describe (3)  |  Ellipse (3)  |  Equation (46)  |  Magnitude (14)  |  Straight Line (4)  |  Unknown (40)

[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.
— Pierre de Fermat
'Relation of New Discoveries in the Science of Numbers', in Letter (Aug 1659) to Pierre de Carcavi, an amateur mathematician, collected in OEuvres de Fermat: Correspondance, 436. Translation, used as an epigraph, in D.M. Burton, Elementary Number Theory (1976, 1989), 107.
Science quotes on:  |  Ancient (27)  |  Everything (38)  |  Know (25)  |  Posterity (11)  |  Show (13)  |  Thank (3)

To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
[Known as Fermat's Last Theorem, the proof of which remained elusive until 1994.]
— Pierre de Fermat
Theorem, beside the eighth proposition of the second book of Diophantus, in Précis des Oeuvres Mathématiques de P. Fermat et de l'Arithmetique de Diophante (1853), 53-54. As translated by Vera Sandford in David Eugene Smith, A Source Book in Mathematics (1929), 212.
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Quotes by others about Pierre de Fermat (5)

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can wasily 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 pricipal 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.
Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.
Science quotes on:  |  Theorem (34)

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.
Quoted in interview for PBS TV program Nova. In William Byers, How Mathematicians Think (2007), 1.
Science quotes on:  |  Determination (37)  |  Distraction (2)  |  Focus (6)  |  Problem (180)  |  Proof (136)  |  Theorem (34)

Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Pascal, 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.
History of Mathematics (3rd Ed., 1901), 366.
Science quotes on:  |  Ability (37)  |  Anecdote (15)  |  Isaac Barrow (6)  |  Calculus (14)  |  Construct (6)  |  Discovery (360)  |  Enable (10)  |  Foreshadow (2)  |  Johannes Kepler (43)  |  Language (71)  |  John Napier (2)  |  Sir Isaac Newton (176)  |  Blaise Pascal (22)  |  Principle (97)  |  Publication (75)  |  John Wallis (2)

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.
From interview for PBS website on the NOVA program, 'The Proof'.
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[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.
Quoted, without source, in The Grolier Library of Science Biographies (1996), Vol. 3, 191.
Science quotes on:  |  Application (72)  |  Broad (7)  |  Elsewhere (3)  |  Exceptional (2)  |  General (26)  |  Idea (226)  |  Intelligent (5)  |  Rule (52)


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  • todayinsci icon 17 Aug - short biography, births, deaths and events on date of Fermat's birth.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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