Fermat's Last Theorem: Simplicity and Complexity

Fermat's Last Theorem: Simplicity and Complexity

Report by Marie (L6) -

On Friday 3 November, the Lower 6th had the pleasure of listening to an intriguing lecture by the Head of Mathematics at Queen Anne's School, titled "Fermat’s Last Theorem: Simplicity and Complexity." Mr Bottomley gave us an introduction to the story of one of history's greatest mathematical challenges - a problem so simple it can be understood by a child, but so complex that it defeated the greatest minds of the past few hundred years.

Many students thought the lecture would consist almost entirely of maths, but this was not the case (to some people's relief!). The story involved murder, misogyny, the Simpsons, several hundred years of passionate problem solving, and financial reward. All the greatest mathematicians were involved, even a few of those before Fermat's time. They all tried to prove the theory, but failed ... until someone solved the problem less than 25 miles from here at Queen Anne's.  

The puzzle was started by Pierre de Fermat, a mathematician in the 17th century, and the theory is: "For any prime number (p) and any integer (a) such that p does not divide a (the pair are relatively prime), p divides exactly into a^p - a". In simpler terms: there are no natural numbers (1,2,3,...) x,y, and z such that x^n + y^n = z^n, in which n is a natural number greater than 2. Many, many mathematicians had a go at trying to the prove the theory, but all failed. Sophie German had a go, even though she had to falsely identify herself using a male name to cover up the fact that she was a female mathematician, which was strictly forbidden in her time. Lewis Carrol had a go, but also failed. Most of us were very surprised that Lewis Carrol was actually a mathematician, as he is most commonly known as the author of "Alice in Wonderland". We also learned an interesting and little known facts that many writers of the Simpsons are mathematicians. Paul Wolfskehl even offered a reward of 100,000 German Mark (an estimated worth of roughly £1 million at the time), but no one managed to solve the problem.

The beginning of the end of the mystery started roughly 100 miles from Caversham in 1963, when the ten year old boy, Andrew Wiles from Cambridgeshire, borrowed a book in his local library. Since then, Andrew Wiles had the life goal of proving the theorem, and when he was thirty he finally managed it, with 130 pages of evidence. However, one year later, someone found a problem in his proof. Wiles had spent just under ten years of his life solving this problem, and he was severely dedicated towards it. His wife said that he would not talk to her at all whilst he was solving the problem, to maintain his concentration. He was about to give up but he pulled it back together and a year later he submitted his new proof, and this time it passed scrutiny. Mr Bottomley showed us a video presenting Andrew Wiles and his office where he solved the problem. Wiles teared up even just thinking about the day he solved the problem. We could see in the background of the video that Wiles's desk had thousands of pieces of paper scattered all around, and Mr Bottomley made a joke that if someone tells you that you should tidy up your desk because you cannot work in a messy environment, that clearly is not true because Wiles worked for multiple years on an overly chaotic desk.

The lecture was ended with a brief overview of what we can learn from Andrew Wiles's journey, and also with a book recommendation titled "Arithmetica", which is even available in the library at Queen Anne's. We learned that passion, resilience and determination are crucial in solving problems in any aspect of life, and that one should never be put off by others' failures.