怀尔斯证明费马大定理的过程

怀尔斯证明费马大定理的过程
Fermat's Last Theorem states that, for any integer n greater than 2, there are no positive integers a, b, and c such that an + bn = cn.
Pierre de Fermat first proposed the theorem in 1637, but it was not until 1995 that Andrew Wiles finally proved it. Wiles' proof was a long and complex one, involving several major mathematical breakthroughs.
First, Wiles developed a strategy for attacking the theorem. He realized that it could be broken down into two distinct parts: the modularity theorem and the Taniyama-Shimura conjecture. The modularity theorem states that certain types of equations can be solved using the properties of modular forms. The Taniyama-Shimura conjecture states that any elliptic curve equation can be written as a modular form.
Wiles then set out to prove each part of the theorem separately. To prove the modularity theorem, he used a mathematical technique called the "Langlands Program". This program involves a series of complex mathematical equations that can be used to solve the modularity theorem.
Next, Wiles used the modularity theorem to prove the Taniyama-Shimura conjecture. He used a technique called "Iwasawa theory", which involves taking a series of equations and solving them simultaneously. This allowed him to prove that any elliptic curve equation can be written as a modular form.
Finally, Wiles used the Taniyama-Shimura conjecture to prove
Fermat's Last Theorem. He used a mathematical technique called the "Faltings theorem" to prove that no positive integers a, b, and c exist such that an + bn = cn.
Wiles' proof of Fermat's Last Theorem was a major breakthrough in mathematics. His proof involved a series of complex mathematical equations and techniques, and it took him several years to complete. It was a major achievement, and it is now considered one of the most important results in mathematics.。