Fermat's Last Theorem
Fermat's Last Theorem is perhaps one of the most famous problems in the history of mathematics. It is a problem that had intrigued mathematicians for over 350 years until finally being solved in 1994 by Andrew Wiles. In this article, we will explore the history of the problem and the solution that finally cracked it.
The Problem
The theorem was first stated by Pierre de Fermat in 1637 in a letter he wrote to his friend, the mathematician Marin Mersenne. Fermat claimed that he had a proof that showed that there are no whole number solutions to the equation:
where is a whole number greater than 2.
Fermat did not provide a proof for his claim, but instead wrote in the margin of his copy of Diophantus' Arithmetica that he had "discovered a truly remarkable proof which this margin is too small to contain." This claim led to a search for a proof that lasted for over three centuries.
Attempts to Solve the Problem
Over the years, many mathematicians attempted to prove Fermat's Last Theorem, but all of them failed. One of the most famous attempts was made by Leonhard Euler, who showed that the theorem was true for , but was unable to extend this to higher values of .
Another attempt was made by Sophie Germain, who worked on the problem for many years in the late 18th and early 19th centuries. She made significant progress by introducing a new mathematical technique called "Fermat's method of infinite descent". However, despite her efforts, she was unable to completely solve the problem.
The Solution
Finally, in 1994, Andrew Wiles, a British mathematician, announced that he had finally solved Fermat's Last Theorem. Wiles' proof was based on the work of many mathematicians who had come before him, including Euler and Germain, and on the use of complex mathematical techniques that were not available to earlier mathematicians.
Wiles' proof is over 100 pages long and relies heavily on advanced algebraic geometry and number theory. The proof was initially met with skepticism by some mathematicians, but it was eventually accepted as correct.
Conclusion
Fermat's Last Theorem is a testament to the power and persistence of mathematical inquiry. It is a problem that stumped some of the greatest minds in mathematics for over three centuries, but it was eventually solved through the combined efforts of many mathematicians and the use of advanced mathematical techniques. Today, Fermat's Last Theorem is considered one of the most important theorems in the history of mathematics and a symbol of the power of human curiosity and ingenuity.
Andrew Wiles, who developed a proof for Fermat's Last Theorem in 1994.