The Historic Photo
The announcement of the proof of Fermat's Last Theorem is a momentous event in the documentary, but the problem was how to show it on screen. Fortunately, one of the mathematicians who attended the lecture when Andrew Wiles revealed his proof was sharp enough to grab a historic photograph. Professor Peter Goddard caught the moment in one of the most charming pictures in the history of mathematics. You can see it at the Plus website.

Andrew Wiles - not a fan of TV
Professor Wiles, having being overwhelmed by the
press attention, was not looking forward to the
prospect of a TV documentary. One of the most persuasive arguments was that this was a unique opportunity to create something that would inspire a new generation of mathematicians. Eventually he agreed to set aside the time required, which turned out to be
three days of discussion prior to filming and five half days of filming. I suspect that Andrew was anxious about what the final film would look like, but in end he was delighted with the documentary. And that has
been one of the great outcomes - the public enjoyed the programme, but mathematicians have praised it as well.

Dark Mansion Story
"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 precede them." This is how Andrew Wiles describes the process of doing mathematics. This was a crucial tale for the documentary because it conjured up such strong imagery. The story appears at the start of the documentary and the imagery returns later, whenever Wiles is in trouble.

Non-Linear Editing
When I started in television in 1991, some people edited by cutting strips of film. But I was part of the video generation. We would sit surrounded by video tapes and take bits from each one, which would all be recorded onto an output tape. The problem was that once a sequence has been recorded, it was impossible to insert anything without starting from scratch. By the time we were making Fermat's Last Theorem, we were in the age of digital editing or non-linear editing. Hundreds of film clips were digitised and stored on a computer, and then they could be manipulated just like text in a word processor. Non-linear editing allows instantaneous cutting and pasting, which means you can experiment much more than you could have done with previous techniques. Some of the fast-cut montages would probably not have occurred had the editing not made experimentation so easy. Today, non-linear editing is available on home PCs, and current home editing is probably on a par with professional editing in the mid-1990s.

The Plot Twist
The story of Andrew Wiles and Fermat's Last Theorem is wonderful for many reasons, and one of them is that is contains a major plot twist. After seven years of secret research, Wiles announces his proof. The mathematical community rejoices. Just when it seems that the story has come to an end, everything falls apart - there is a flaw in the proof. This is akin to typical horror movie, whereby the hero slays the monster, and just as he turns his back the monster comes back to life for one last attack. Fortunately for Wiles, he slayed the monster at the second attempt and emerged triumphant. From a director's point of view, it is a huge bonus to have such a major plot twist two thirds of the way through a documentary. I am glad that the original proof was flawed.