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NOVA : Usually people work in groups and use each other for support. What did you do when you hit a brick wall?

AW : When I got stuck and I didn’t know what to do next, I would go out for a walk. I’d often walk down by the lake. Walking has a very good effect in that you’re in this state of relaxation, but at the same time you’re allowing the sub-conscious to work on you. And often if you have one particular thing buzzing in your mind then you don’t need anything to write with or any desk. I’d always have a pencil and paper ready and if I really had an idea I’d sit down at a bench and I’d start scribbling away.

NOVA : So for seven years your pursuing this proof. Presumably their are periods of self-doubt mixed with the periods of success.

AW : Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it’s completely dark. You stumble around bumping into the furniture but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of , and couldn’t exist without, the many months of stumbling around in the dark that proceed them.

NOVA : And during those seven years, you could never be sure of achieving a complete proof.

AW : I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal. It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years. So even if I was on the right track, I could be living in the wrong century.

NOVA : Then eventually in 1993, you made the crucial breakthrough.

AW : Yes, it was one morning in late May my wife, Nada, was out with the children and I was sitting at my desk thinking about the last stage of the proof. I was casually looking at a research paper and there was one sentence that just caught my attention. It mentioned a nineteenth century construction, and I suddenly realised that I should be able to use that to complete the proof. I went on into the afternoon and I forgot to go down for lunch, and by about three or four o’clock I was really convinced that this would solve the last remaining problem. It got to about tea time and I went downstairs and Nada was very surprised that I’d arrived so late. Then I told her - I’d solved Fermat’s Last Theorem.

NOVA : The New York Times exclaimed “At Last Shout of “Eureka!” in Age-Old Math Mystery”, but unknown to them, and to you, there was an error in your proof. What was the error?

AW : It was an error in a crucial part of the argument, but it was something so subtle that I’d missed it completely until that point. The error is so abstract that it can’t really be described in simple terms. Even explaining it to a mathematician would require the mathematician to spend two or three months studying that part of the manuscript in great detail.

NOVA : Eventually, after a year of work, and after inviting the Cambridge mathematician Richard Taylor to work with you on the error, you managed to repair the proof. The question that everybody asks is this - is your proof the same as Fermat’s?

AW : There’s no chance of that. Fermat couldn’t possibly have had this proof. It’s 150 pages long. It’s a 20th century proof, it couldn’t have been done in the 19th century, let alone the seventeenth century. The techniques used in this proof just weren’t around in Fermat’s time.

NOVA : So Fermat’s original proof is still out there somewhere.

AW : I don’t believe Fermat had a proof. I think he fooled himself into thinking he had a proof. But what has made this problem special for amateurs is that there’s a tiny possibility that there does exist an elegant seventeenth century proof.

NOVA : So some mathematicians might continue to look for the original proof. What will you do next?

AW : There’s no problem that will mean the same to me. Fermat was my childhood passion. There’s nothing to replace it. I’ll try other problems. I’m sure that some of them will be very hard and I’ll have a sense of achievement again, but nothing will mean the same to me - there’s no other problem in mathematics that could hold me the way that this one did.There is a sense of melancholy. We’ve lost something that’s been with us for so long, and something that drew a lot of us into mathematics. But perhaps that’s always the way with math problems, and we just have to find new ones to capture our attention. People have told me I’ve taken away their problem - can’t I give them something else? I feel some sense of responsibility. I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.

NOVA : What is the main challenge now?

AW : The greatest problem for mathematicians now is probably the Riemann Hypothesis. But it’s not a problem that can be simply stated.

NOVA : And is there any one particular thought that remains with you now that Fermat’s Last Theorem has been laid to rest?

AW : Certainly one thing that I’ve learned is that it is important to pick a problem based on how much you care about it. However impenetrable it seems, if you don’t try it, then you can never do it. Always try the problem that matters most to you. I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream. I know it’s a rare privilege, but if one can really tackle something in adult life that means that much to you, then it’s more rewarding than anything I can imagine.

NOVA: And now that journey is over, there must be a certain sadness?

AW : There is a certain sense of sadness, but at the same time there is this tremendous sense of achievement. There’s also a sense of freedom. I was so obsessed by this problem that I was thinking about if all the time - when I woke up in the morning, when I went to sleep at night, and that went on for eight years. That’s a long time to think about one think . That particular odyssey is now over. My mind is now at rest.

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