Frasi di Pierre de Fermat

Pierre de Fermat è stato un matematico e magistrato francese.

Fu tra i principali matematici della prima metà del XVII secolo e dette importanti contributi allo sviluppo della matematica moderna:



con il suo metodo per la individuazione dei massimi e dei minimi delle funzioni precorse gli sviluppi del calcolo differenziale.

fece ricerche di grande importanza sulla futura teoria dei numeri, iniziate durante la preparazione di un'edizione della Arithmetica di Diofanto di Alessandria, su cui scrisse note ed osservazioni contenenti numerosi teoremi. Proprio in una di queste osservazioni "a margine" enunciò il cosiddetto ultimo teorema di Fermat , che è rimasto indimostrato per più di 300 anni, fino al lavoro di Andrew Wiles nel 1994.

scoprì, indipendentemente da Cartesio, i principi fondamentali della geometria analitica e, attraverso la corrispondenza con Blaise Pascal, fu uno dei fondatori della teoria della probabilità. Wikipedia  

✵ 1601 – 12. Gennaio 1665
Pierre de Fermat photo
Pierre de Fermat: 7   frasi 0   Mi piace

Pierre de Fermat Frasi e Citazioni

“È impossibile scrivere un cubo come somma di due cubi o una quarta potenza come somma di due quarte potenze o, in generale, nessun numero che sia una potenza maggiore di due può essere scritto come somma di due potenze dello stesso valore. Dispongo di una meravigliosa dimostrazione di questo teorema che non può essere contenuta nel margine troppo stretto della pagina.”

Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et 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.
Origine: Dal margine della sua copia del libro II dellAritmetica di Diofanto di Alessandria; citato in Simon Singh, L'Ultimo Teorema di Fermat, traduzione di Carlo Capararo e Brunello Lotti, Milano, Rizzoli, 1997, p. 89. ISBN 8817845280

Pierre de Fermat: Frasi in inglese

“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.”

Et cette proposition est généralement vraie en toutes progressions et en tous nombres premiers; de quoi je vous envoierois la démonstration, si je n'appréhendois d'être trop long.
Fermat (in a letter dated October 18, 1640 to his friend and confidant Frénicle de Bessy) commenting on his 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).

“I have discovered a truly remarkable proof of this theorem which this margin is too small to contain.”
Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet.

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

“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”

Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, The Pell Equation http://books.google.com/books?id=L6QKAAAAYAAJ (1912)
Contesto: 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.

“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?”

Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, The Pell Equation http://books.google.com/books?id=L6QKAAAAYAAJ (1912)
Contesto: 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.

“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 refractions which Monsieur Descartes has established.”

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

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