The mathematician who solved Fermat's Last Theorem delivers a lecture in Dublin this evening on how the deed was done, writes Dick Ahlstrom.
The striking simplicity of a mathematical equation helped convince a young boy to pursue mathematics as a career. The net result of this choice was a solution to a 350-year-old mathematical puzzle that no one believed could be solved.
Such is the tale to be told this evening by Prof Andrew Wiles of Princeton University, the mathematician who cracked the best known "insoluble" problem in his field, Fermat's Last Theorem.
Wiles will deliver the annual Hamilton Lecture at Trinity College Dublin. The lecture, named after Ireland's greatest mathematician, William Rowan Hamilton, is organised by the Royal Irish Academy and The Irish Times and is sponsored by DEPFA Bank plc.
Prof Wiles's lecture is entitled, Solving Equations. It will include an account of how he came to solve Fermat's impossible theorem but also discuss the whole business of solving insoluble equations. No tickets remain for his sell-out lecture.
"Solving equations is an activity that is as old as recorded history," he said yesterday. Babylonian and Greek mathematicians left behind many examples for later mathematicians to solve. "The frustration is they are very simple to state but have stymied human kind for centuries."
Fermat's Theorem was a case in point. It is simplicity itself in stating that xn + yn = zn where x, y and z have no non-zero integer solutions when n is greater than two. Put in the mid-17th century, generations of mathematicians decided it was not provable until Wiles came along with a published proof in 1995.
Wiles saw the theorem as a 10-year-old while perusing a maths book in a local library. "I think I already was fascinated with mathematics but it convinced me it was a field one could spend one's life doing," he says.
He puzzled over the problem while still a teenager but left it to pursue degrees in mathematics, studying in Britain, Germany and the US. He settled into a position at Princeton University and left Fermat alone until he encountered work by other mathematicians on something known as the Shimura-Taniyama Conjecture. "What it did for me was I could approach Fermat from a completely new angle and I had no doubt it would solve the equation," he explains.
He at once began an eight-year struggle, first with the Conjecture and then with Fermat's Theorem. "There were a lot of ingredients in linking the two conjectures," he admits. He got close to a proof of Fermat in 1993 but there was a subtle error. "I thought I had it and there was this terrible period of about a year trying to resuscitate it. The strategy was right but this key ingredient wasn't working."
He reached a low point believing that perhaps the theorem wasn't soluble, but he persisted, hoping to prove to himself, once and for all, that it couldn't be done. In the process however, he had a breakthrough and finally proved Fermat's Last Theorem.
He is somewhat taken aback when asked how the project could so captivated his mind. "How could it not captivate someone's mind," he suggested, such was its simplicity and beauty.
Now he is back in the business of solving "impossible" theorems. "I have to try the big problem," he says. "I can't resist it. But you have to be realistic too."
Nor will there be any difficulty finding new challenges. "The great thing about number theory is there are always problems, you don't have to look for them." Top of his list is the "impossible" Riemann Hypothesis.
Prof Wiles will this evening present the RIA/DEPFA Bank Hamilton prize in mathematics awards to mathematics students in each of Ireland's nine universities. These awards are given to the best student in their second-last year and each receives a cheque for EUR1,000. The winners, to be announced later today, are: Arthur Prendergast (Trinity College Dublin); Catherine Hayes (NUI Maynooth); Donough Regan (University College Dublin); Eamon Loughnane (Dublin City University); Daniel Hurley (NUI Galway); Catherine Leeman (Queen's University Belfast); Ian Walsh (University of Ulster); Colm Fitzgerald (NUI Cork); and Mairead Crowe (University of Limerick).