Fermat's Last Theorem is a mathematical theorem proposed by Pierre de Fermat in 1637. It 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 2. In other words, there are no whole number solutions to this equation.
Fermat's Last Theorem is significant because it is one of the most famous and long-standing problems in mathematics. It has been studied and attempted to be solved by many mathematicians over the centuries, and its proof was finally provided in 1994 by Andrew Wiles.
The proof for Fermat's Last Theorem is a complex and lengthy mathematical proof that involves many advanced concepts such as elliptic curves, modular forms, and Galois representations. Andrew Wiles spent years working on the proof and it has been reviewed and accepted by the mathematical community.
Fermat's Last Theorem is also known as "Nobody Understands Me" because of a note written by Pierre de Fermat in the margin of his copy of the book "Arithmetica" by Diophantus. He claimed to have a proof for the theorem that was too large to fit in the margin, but never actually provided the proof or any further explanation.
Fermat's Last Theorem has no direct practical applications. However, the methods and techniques used to prove it have been applied to other areas of mathematics and have led to important developments in number theory and algebraic geometry.