| Fermat's Theorem |
Historical Summary |
In
respect to the historical authenticity, it is imperious that the statement of the
celebrated Fermat’s theorem (also denominated “the big” or “the
last”) is transcribed, in its original form, that is, with the composition that the
proper Pierre Fermat gave to it, in manuscript, on the margin of one the pages of a copy
of Diophante’s works, published, to that time, by Cachet de Meziriac: “Cubus
in duos cubus aut quadrato-quadratum in duos quadrato-quadratos et generalitir
nullam in infinitum, ultra-quadratum, potestarem in duas ejusdecem nominis faz est
dividire.
Cujus rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non
carperet.” The date in which Pierre Fermat would have obtained the demonstration of his great theorem is imprecise. It should be understood between 1626, year that Bachet de Meziriac had published the Diophante’s works, and 1665, that was the year of his death; more approximately, after 1659, year when he would have demonstrated the restricted proposition, for n = 3, communicating it to Carcavi, in epistolary correspondence. Surely that notable
event would have been verified in more than three centuries !... Verifying the
veridicalness of this mathematical proposition comes constituting itself for such long
time, in fantastic and inebriating challenge to the marvellous human intelligence! More exactly, it causes
inebriating astonishment that, in such long period an exact and generical demonstration of
that mathematical proposition has not gotten discovered, of such simple appearance,
nevertheless the extended efforts of an plead of illustrious and renowned mathematicians:
Euler, Legendre, Lejeune-Dirichlet, Gauss, Sophie-Germain, Lamé, Liouville, Cauchy,
Kummer, Kronecher, Kornecker, Abel, Matheus, Catalan, E.Lucas, Mirimanoff, Sylvester,
Dickson, Wieferich, Frobenius, Fabry, Cahen, Leon Pomey, Vandiver, Mordell F. Beukers, H.
M. Edwards, S. Lang, Paulo Ribenboim, R. Wait, etc. On these three elapsed
centuries, from the popularization of the enunciated proposition of the famous
Fermat’s theorem, a disputation was settled down, until nowadays, for successive
generations of illustrious mathematicians among the ones mentioned above. In the 19th century, for several decades, the National Academy of Sciences, from France, offered a honorary award to whom presented an exact and generical demonstration for mentioned Fermat’s proposition. Just unsuitable or
partial works, valid demonstrations for mentioned proposition, exclusively, for certain
categories of prime numbers lower to certain limits (limits more and more enlarged,
reaching the hundreds of digits), they were disclosed or presented to that Institution. That Academy had
finished for suppressing the offer of the prize, awarding it to the illustrious German
mathematician Kummer, for the presentation of his original and marvellous “Theory of
the Ideal Prime Numbers”, for which he, Kummer, has approached a lot of facets of the
intrinsic nature of the Fermat’s problem. In the beginning of the
current century, an endowment of 100.000 German marks was offered by University of Göttingen, by the illustrious
German scientist, Doctor Paul Wolfskehl, so that he instituted a prize to be offered to
the international scientifically community, what was made by that University, under a
rigid and pertinent regulation, thoroughly disclosed. Among the countless
candidates to the conquest of this distinguished award, it is worth to mark: Antônio Moreira Calaes Emeritus Professor from Escola de Minas from Universidade Federal de Ouro Preto |
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