Image credit: John Cairns
One of the world’s most celebrated mathematicians, Sir Andrew Wiles, is widely known as the man who cracked Fermat’s Last Theorem.
In 1994 Andrew’s proof catapulted him to international fame. He went on to earn some of mathematics’ highest honours, including the Abel Prize and a Copley Medal from the Royal Society. Both his peers and the wider world were gripped by his solving of what was widely believed to be an 'impossible' problem. In 1637 Fermat had stated that there are no whole number solutions to the equation xn + yn = zn when n is greater than 2, unless xyz=0. Fermat went on to claim that he had found a proof for the theorem, but said that the margin of the text he was making notes on was not wide enough to contain it.
At a rare public appearance earlier this week, at the Inaugural Oxford Mathematics London Public Lecture, held in the Science Museum, the audience were treated to revealing insight in to the man behind the maths.
Hosted by mathematician and broadcaster Dr Hannah Fry of University College London, the event featured a lecture followed by an interview including Andrew taking questions from the floor. In front of an audience that included the TV presenter Dara Ó Brian, Andrew addressed a range of questions and shared his thoughts and feelings on everything from his own personal career challenges to the role of maths in society at large.
Answering the question ‘is mathematical skill more nature than nurture?’ he drew a comparison with the film Good Will Hunting, which it is implied that if you are born with a natural aptitude for mathematics, it is easy. ‘There are some things that you are born with that might make it easier, but it is never easy", he said.
‘Mathematicians struggle with mathematics even more than the general public does. We really struggle. It’s hard. But we learn how to adapt to that struggle.’ Of his own struggles, Andrew revealed his belief in the ‘three Bs: Bus, bath and bed.’ Time when you can give into your subconscious and the mind is free to wander away from the immediate problem.
Asked by the comedian Dara Ó Brian, to describe his progress tackling Fermat’s problem, he compared it to three flagpoles in a row, ‘each one higher than the other’ but the ropes that join them ‘sort of sink’ with a ‘particularly big sag in the last one.’
Andrew also talked about his motivations. On the influences that drove his success in proving Fermat’s Last Theorem, and that continue to drive him today, he said: ‘I am always quite encouraged when people say something like: ‘You can’t do it that way.’
When asked his opinion on the skills required to be a great mathematician, he said that he believes that success in the field is more down to character than technical skill. ‘You need a particular kind of personality that will struggle with things, will focus and won’t give up.’ Sometimes the best young mathematicians can’t adapt to this need for struggle, he said. They want to solve things in days. Sometimes it takes much, much longer.
As a specialist in number theory, was he ever tempted to explore other mathematical fields? The answer was an unequivocal ‘no.’ He fell in love with his chosen specialism at a young age and his commitment has never wavered. ‘I confess that I was addicted to number theory from the time I was 10 years old and I have never found anything else in mathematics that appealed quite as much.’
When pressed as to whether his loyalty may be due to feeling less able in other areas, he added ‘definitely true.’
On the subject of exactly what it was that intrigued him most about Fermat’s theorem, he said that he was most captivated by the fact that Fermat wrote down the problem in a copy of a book of Greek Mathematics. ‘It was only found after his death by his son.’
He was so intrigued by the problem that as a student he would ‘sneak off to the library’ to read Fermat. But getting to grips with Fermat did not come easily to him. ‘He had this really irritating habit of writing in Latin.’ To this day Andrew’s Latin remains ‘minimal’.
Pressed on his view on one of the most challenging educational issues, the quality of and attitude towards mathematics at school and in the wider population, he cautioned that the issue is not that children are less interested in maths. ‘Most young people do have a real appetite for mathematics but they are put off by uninspiring teaching.’ When the teachers are not interested in the subjects they teach, it shows and rubs off and ‘gets passed on’ to their students. This is a particular problem at primary level where few of the teachers are mathematicians. As for a potential solution to the ongoing teaching crisis Andrew suggested ‘pay them more.’
Encouraging great mathematicians of the future, he advised them to tackle the ‘impossible problems’ while they were young (teens or undergraduates) and get a taste for research. But, they should buckle-down and ‘be responsible’ when they start their careers.
Andrew also discussed the Millennium Prize Problems, seven mathematical problems that were set by the Clay Mathematics Institute 17 years ago, offering $1 million dollar rewards for each one solved.
One of the problems, the Poincaré conjecture had already been solved in 2003, and of the remaining six, Andrew suggested the Riemann hypothesis is receiving the most attention. First identified by the German mathematician David Hilbert in 1900, the problem ‘says something about the way prime numbers are distributed’ a field where number theorists across the world have been collaborating with huge success over the past two decades.
Andrew shared his view of the beauty of mathematics and what this actually means. He compared solving a mathematical conundrum to walking down a path to explore a garden, designed by the great landscape architect Capability Brown and seeing a new and breathtaking view for the first time. The real thrill is in ‘this surprise element of suddenly seeing everything clarified and beautiful.’
But, like any thing of beauty, you should not stare at a mathematical problem for too long, otherwise ‘the majesty will fade, as is the case with great paintings and music.’ Instead, he prefers to ‘keep walking’ through the garden of mathematics, rediscovering his life’s passion, again and again.