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An English professor just won $700,000 for solving a 379-year-old maths problem

Think your calculus homework is hard? This problem took centuries to solve.

PETER DOCKRILL
17 MAR 2016
 

As a 10-year-old boy in the 1960s, Andrew Wiles happened across a book in his local library called The Last Problem, which detailed a ~330-year-old struggle to solve the most longstanding unsolved problem in the history of mathematics: Fermat's Last Theorem.

Decades later, the now Sir Andrew Wiles – a professor of mathematics at the University of Oxford in the UK – has been awarded the prestigious Abel Prize for 2016, likened to the Nobel Prize of the math world. The award, bestowed by the Norwegian Academy of Science and Letters, carries with it a cash prize worth more than US$700,000, which some might say isn't such an extravagant reward for a proof described as "an epochal moment for mathematics".

 

Once he laid eyes upon Fermat's Last Theorem, the young Wiles was hooked on solving it, although he could never have guessed that the challenge would occupy the next three decades of his life.

"This problem captivated me," Wiles told Ian Sample at The Guardian. "It was the most famous popular problem in mathematics, although I didn't know that at the time. What amazed me was that there were some unsolved problems that someone who was 10 years old could understand and even try. And I tried it throughout my teenage years. When I first went to college I thought I had a proof, but it turned out to be wrong."

Put simply, the theorem, formulated by French mathematician Pierre de Fermat in 1637, states: "There are no whole number solutions to the equation xn+yn=zn when n is greater than 2."

While the theorem can be expressed in such simple terms, solving it vexed mathematicians for some 350 years before Wiles' first proof was delivered in 1993.

That original solution – taking some 200 pages to write down – was the result of an intense period of research lasting seven years, during which Wiles lectured at Princeton University. When he delivered the proof in a series of lectures at Cambridge University, a crowd of some 200 researchers in attendance erupted in applause.

But even then, Fermat wasn't done. A mathematician reviewing Wiles' original work noticed errors in the solution, requiring the proof to be revised.

The final version was published in 1995 with the help of one of Wiles' former students, and the story behind the century-spanning solution generated such interest in the mathematics world (and outside of it) that a book on the saga became an international bestseller.

So how did Wiles solve what others couldn't for hundreds of years? By approaching the problem from an unconventional angle, combining elements of three branches of mathematics – modular forms, elliptic curves, and Galois representations – and building upon the work of centuries of mathematicians before him. Want a wee bit more detail? See here.

Now, with Wiles' latest recognition (he's already won several other awards), it's a fitting end to a race that began centuries ago, when a bold Fermat himself epically teased a solution to the theorem, before claiming that he didn't have enough space in his notes to write it down. "I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain," he wrote. (Fermat's own 'solution' was never found.)

For his part, Wiles says he hopes his efforts will encourage the next generation of curious 10-year-olds to dive into the challenges that mathematics offers.

"It is a tremendous honour to receive the Abel Prize and to join the previous Laureates who have made such outstanding contributions to the field," he said in a statement to the press. "Fermat's equation was my passion from an early age, and solving it gave me an overwhelming sense of fulfilment. It has always been my hope that my solution of this age-old problem would inspire many young people to take up mathematics and to work on the many challenges of this beautiful and fascinating subject."

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