Fermat's last theorem - Early history

The theorem needs only to be proven for n=4 and in the cases where n is an odd prime number.[2] For various special exponents n, the theorem had been proven over the years, but the general case remained elusive. Fermat himself proved the case n=4, while Euler proved the theorem for n=3. The case n=5 was proved by Dirichlet and Legendre in ...

See also:

Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - Early history

This is the note that Fermat wrote in the margin of Arithmetica: Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, 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. (It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly ma ...

See also:

Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - Did Fermat really have a proof?

Fermat's last theorem - Fermat's comment in the Arithmetica. In problem II.8 of his Arithmetica, Diophantus asks how to split a given square number into two other squares (in modern notation, given a rational number k, find u and v, both rational, such that k2 = u2 + v2), and shows how to solve the problem for See also:

Fermat's last theorem, Fermat's last theorem - History, Fermat's last theorem - Fermat's comment in the Arithmetica, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - History

Using sophisticated tools from algebraic geometry (in particular elliptic curves and modular forms), Galois theory and Hecke algebras, the English mathematician Andrew Wiles, from Princeton University, with help from his former student Richard Taylor, devised a proof of Fermat's last theorem that was published in 1995 in the journal Annals of Mathematics. In 1986, Ken Ribet had proved Gerhard Frey's epsilon conjecture that every counterexample an + bn = cn to Fermat's las ...

See also:

Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - The proof

In "The Royale", an episode of Star Trek: The Next Generation, Captain Picard states that the theorem had gone unsolved for 800 years. Wiles' proof was released five years after the particular episode aired. This was subsequently mentioned in a Star Trek: Deep Space Nine episode called "Facets" during June 1995 in which Jadzia Dax comments that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." [4] This reference was generally understood by ...

See also:

Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - Trivia

Fermat's last theorem is a generalization of the Diophantine equation a2 + b2 = c2, which is linked to the Pythagorean theorem. Ancient Chinese, Greeks and Babylonians knew that this equation has integer solutions, such as (3,4,5) (32 + 42 = 52) or (5,12,13). These solutions are known as Pythagorean triples, and there exist an infinite number of them (even excluding trivial solutions for which a, b and c have a common divisor). According to Fermat's last theorem, no such soluti ...

See also:

Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - Mathematical context

In "The Royale", an episode of Star Trek: The Next Generation, Captain Picard states that the theorem had gone unsolved for 800 years. Wiles' proof was released five years after the particular episode aired. This was subsequently mentioned in a Star Trek: Deep Space Nine episode called "Facets" during June 1995 in which Jadzia Dax comments that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." [4] This reference was generally understood by ...

See also:

Fermat's last theorem, Fermat's last theorem - History, Fermat's last theorem - Fermat's comment in the Arithmetica, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - Trivia

There is considerable doubt over whether Fermat's claim to have "a truly marvellous proof" was correct. Wiles's proof is about 200 pages long and beyond the understanding of most mathematicians today. It is quite possible that there is a proof that is both essentially shorter, and more elementary in its methods; initial proofs of major results are typically not the most direct. Math institutions still receive many papers, some say in the thousands, claiming t ...

See also:

Fermat's last theorem, Fermat's last theorem - History, Fermat's last theorem - Fermat's comment in the Arithmetica, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - Did Fermat really have a proof?