Pierre de Fermat's Last Theorem

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17 August 2011

Famous Quote:

"I have a truly marvelous demonstration of this proposition which this margin is too small to contain.""
Pierre de Fermat : 821

(Fermat often scribbled notes in the margin of Bachet's translation of Diophantus's "Arithmetica".)

Fermat's Last Theorem

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For other theorems named after Pierre de Fermat, see Fermat's theorem.

In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than two.
This theorem was first conjectured by Pierre de Fermat in 1637, famously in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. No successful proof was published until 1995 despite the efforts of countless mathematicians during the 358 intervening years. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult maths problems".

tangent: Fermat’s tangent method

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• Fermat’s tangent methodPierre de Fermat anticipated the calculus with his approach to finding the tangent line to a given curve. To find the tangent to a point P (x, y), he began by drawing a secant line to a nearby point P1 (x + ε, y1). For small ε, the secant line PP1 is approximately equal to the angle PAB at which the tangent meets the x-axis. Finally, Fermat allowed ε to shrink to zero, thus obtaining a mathematical expression for the true tangent line.
• CreditEncyclopædia Britannica, Inc.

(I do not understand a single word, but it sounds awfully clever, so I reprint it here!!)

• Links
  • geometry (mathematics)
  • mathematics
  • tangent (mathematical function)
  • Pierre de Fermat (French mathematician)
• CitationsMLA style:
  tangent: Fermat’s tangent method. Art. Encyclopædia Britannica Online. Web. 17 Aug. 2011. <http://www.britannica.com/EBchecked/media/57048/Fermats-tangent-method-Pierre-de-Fermat-anticipated-the-calculus-with>.
  
  
  APA style:
  tangent: Fermat’s tangent method. [Art]. In Encyclopædia Britannica. Retrieved from http://www.britannica.com/EBchecked/media/57048/Fermats-tangent-method-Pierre-de-Fermat-anticipated-the-calculus-with

Fermat, Pierre de (1601-1665)

				French lawyer who pursued mathematics in his spare time. Although he pursued mathematics as an amateur, his work in number theory was of such exceptional quality and erudition that he is generally regarded as one of the greatest mathematicians of all times. He had the habit of scribbling notes in the margins of books or in letters to friends rather than publishing them. He discovered analytic geometry independently of Descartes, but did not publish his work. He founded the theory of probability with Pascal and discovered the least time principle which states that light will travel through an optical system in such a way as to pass from starting to ending point in the least amount of time (a concept from calculus of variations ). Fermat solved many fundamental calculus problems, and made important contributions to number theory and optics. He was also fluent in French, Italian, Spanish, Latin, and Greek. He is most famous for scribbling a note in the margin of a book by Diophantus that he had discovered a proof that the equation xn+yn = zn has no integer solutions for n>2. He stated "I have discovered a truly marvelous proof of this, which however the margin is not large enough to contain." The proposition, which came to be known as Fermat's last theorem, baffled all attempts to prove it until A. Wiles succeeded in 1995. Descartes, Diophantus, Pascal