Pierre de Fermat cytaty

Pierre de Fermat Fotografia
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Pierre de Fermat

Data urodzenia: 17. Sierpień 1601
Data zgonu: 12. Styczeń 1665

Reklama

Pierre de Fermat – matematyk francuski, z wykształcenia prawnik i lingwista, od 1631 radca parlamentu w Tuluzie. Większość jego prac matematycznych została opublikowana dopiero po śmierci przez syna, Samuela. Pierre de Fermat dokonał wielu odkryć w teorii liczb, m.in. sformułował słynne wielkie twierdzenie Fermata. Wykazał, że wszystkie krzywe drugiego stopnia da się uzyskać przez odpowiednie przecinanie płaszczyzną powierzchni stożka; podał metodę znajdowania ekstremum funkcji. Jego prace wraz z pracami Blaise Pascala stworzyły też podstawy pod późniejszy rozwój rachunku prawdopodobieństwa.

Fermat nie publikował swoich odkryć, przez co pozostawały nieznane. Niektóre z nich zostały następnie niezależnie odkryte przez Kartezjusza, co wywołało spór o pierwszeństwo. Było tak m.in. z kartezjańskim układem współrzędnych i wieloma innymi zastosowaniami algebry w geometrii. Fermat już w 1636 wprowadził metodę prostokątnego układu współrzędnych, przeprowadził dowód, że równaniom pierwszego stopnia odpowiadają proste, a równaniom drugiego stopnia linie odpowiadające przecięciu stożka płaszczyzną . Spór między Fermatem a Kartezjuszem zakończył się ostatecznie pogodzeniem obu uczonych i wzajemnym uznaniem zasług. Obecnie obaj uznawani są za ojców geometrii analitycznej.

Podobni autorzy

Cytaty Pierre de Fermat

„Znalazłem zaiste zadziwiający dowód tego twierdzenia. Niestety, margines jest zbyt mały, by go pomieścić.“

— Pierre de Fermat
notka na marginesie łacińskiego tłumaczenia książki Arithmetica Diofantosa, dotyczy wielkiego twierdzenia Fermata.

„I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof“

— Pierre de Fermat
Context: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square. Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, [http://books.google.com/books?id=L6QKAAAAYAAJ The Pell Equation] (1912)

Reklama

„There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically?“

— Pierre de Fermat
Context: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square. Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, [http://books.google.com/books?id=L6QKAAAAYAAJ The Pell Equation] (1912)

„The result of my work has been the most extraordinary, the most unforeseen, and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses, and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the s which Monsieur Descartes has established.“

— Pierre de Fermat
Epist. XLII, written at Toulouse (Jan. 1, 1662) and reprinted in Œvres de Fermat, ii, p. 457; i, pp. 170, 173, as quoted by , A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century (1910) [https://books.google.com/books?id=CGJDAAAAIAAJ&pg=PA10 p. 10.]

„I have discovered a truly remarkable proof of this theorem which this margin is too small to contain.“

— Pierre de Fermat
Note written on the margins of his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus, this was taken as an indication of what became known as Fermat's last theorem, a correct proof for which would be found only 357 years later; as quoted in Number Theory in Science and Communication (1997) by Manfred Robert Schroeder

„And this proposition is generally true for all progressions and for all prime numbers; the proof of which I would send to you, if I were not afraid to be too long.“

— Pierre de Fermat
Fermat (in a letter dated October 18, 1640 to his friend and confidant Frénicle de Bessy) commenting on his statement<!--Fermat's statement--> that p divides a<sup> p−1</sup> − 1 whenever p is prime and a is coprime to p (this is what is now known as Fermat's little theorem).

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