Fermat’s last theorem Currently holding the world record for longest standing math problem ever, Fermat’s last theorem went unsolved for 365 years. Fermat’s last theorem was one of the largest white whales in the study of math. Over the centuries, thousands were puzzled by the impossible problem. From its conception to its solution, Fermat’s last theorem was one of the most difficult to solve yet easy to understand problems in mathematics. First, I will discuss the theorem and how it was introduced to the mathematics community.
Second, I will discuss some of the influences Fermat’s last theorem has had over its lengthy history. Third, I will discuss how solution finally came about. Fermat was a seventeenth century judge who spent his spare time tinkering in mathematics. He came up with a variety of mathematical proofs which he wrote in the margins of his copy of the Arithmetica, a mathematics book from ancient Greece. He wrote many theorems and notes within the margins of that book. The most famous of which came to be known as Fermat’s last theorem.
Translated from Latin Fermat wrote “It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain. ” () After the death of his father Fermat’s son discovered the copy of the Arithmetica containing many of Fermat’s notes and theorems. He reprinted the Arithmetica with Fermat’s notes included.
Many mathematicians read the reprinting which claimed Fermat had discovered proofs for several of his own theorems yet Fermat never published any of them. Seeing these claims each of Fermat’s theorems received a proof either proving or disproving the theorems. All except one. The last of Fermat’s theorems to receive a proof, then began to trouble and inspire mathematicians through the centuries. Many people were able to prove the theorem for specific exponents or make other contributions to the study as time passed, but no one was able to find a proof for the theorem.
Many of them have interesting stories, but one was particularly memorable. Over a century after Fermat a mathematician named Paul Wolfskehl was on the verge of suicide. Wolfskehl had set his death for precisely midnight at which time he would shoot himself through the head. He decided to pass the last few hours reading about the latest on developments in Fermat’s theorem. As he read Wolfskehl began to get an idea for a solution to the theorem. He began to explore this new approach to the solution. By the time he realized this new avenue was a dead end the appointed time of Wolfskehl’s demise had long passed.
Wolfskehl went on to continue study in mathematics, saying that Fermat’s theorem reminded him of the beauty in number theory. Wolfskehl went on to change his will saying that whoever solved the problem 100,000 the equivalent of two million in today’s currency. After his death the Wolfskehl prize was announced. In the first year of the prize 621 proofs were sent in to be evaluated and all of them were flawed. Mathematical historian Howard Eves once said, “Fermat’s Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published. (Howard Eves)
While those proofs were wrong a correct proof was just over the horizon. Three centuries after the theorem had been first written a ten year old boy named Andrew Wiles was checking out a book from the library. The book had been written about the theory behind Fermat’s last theorem. Andrew Wiles, after reading this book, became infatuated with the challenge such a math problem represented. He never stopped learning and wondering about this seemingly impossible problem even after earning a PhD in mathematics.
Discovering that another theorem, the Taniyama-Shimura Conjecture, included Fermat’s last theorem as part of the projected solution, Wiles began work on a proof that would solve the conjecture and this multicentury theorem. He spent seven years working on a proof before finally publishing his work. He was celebrated as one of the greatest mathematician of the era. He then gave a lecture at the Isaac Newton Institute for Mathematical Sciences over the course three days explaining his proof of the Taniyama-Shimura Conjecture.
Unfortunately, there was a mistake in the proof. A problem that Wiles had overlooked completely destroyed the proof. Not one to give up Andrew Wiles returned to the drawing board to try and work around the problem. Wiles spent a year trying to solve the problem in the proof when a flash of inspiration hit him, allowing wiles to finish his proof and republish. This time Wiles’ proof stood up to peer review making Wiles the first person to officially solve this proof that befuddled and inspired thousands. Today I discussed the origins of Fermat’s last theorem.
Secondly, I discussed the influence of the theorem over the ages. Finally, I discussed how this theorem was finally solved by a person inspired by the theorem to enter mathematics. Fermat’s last theorem was one of the most difficult yet easy to understand problems in mathematics. When most people think of math they think about numbers and difficult classes in school, but to those who understand the nature of math there is so much more to it than what the surface shows, like a simple theorem that couldn’t be solved for hundreds of years.