I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.

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.

That particular odyssey is now over. My mind is now at rest.

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

However impenetrable it seems, if you don't try it, then you can never do it.

Fermat said he had a proof.

Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.

Always try the problem that matters most to you.

Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve.

Pure mathematicians just love to try unsolved problems - they love a challenge.

The greatest problem for mathematicians now is probably the Riemann Hypothesis.

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.

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.

I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.

I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream.

I realized that anything to do with Fermat's Last Theorem generates too much interest.

The only way I could relax was when I was with my children.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.

But the best problem I ever found, I found in my local public library.

Just because we can't find a solution it doesn't mean that there isn't one.

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.

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.

I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.

Then when I reached college I realized that many people had thought about the problem during the 18th and 19th centuries and so I studied those methods.

I was so obsessed by this problem that I was thinking about it all the time - when I woke up in the morning, when I went to sleep at night - and that went on for eight years.

I loved doing problems in school.

It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.

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.

There are proofs that date back to the Greeks that are still valid today.

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.

I loved doing problems in school. I'd take them home and make up new ones of my own. But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem - Fermat's Last Theorem.

Pure mathematician just love to try unsolved problems they love a challenge.

My goal is, of course, for this show to do well, and I would love it if people liked it.

A goal without a plan is just a wish.

The best thanks we could offer those who went before and raised the Irish working class from their knees was to press forward with determination and enthusiasm towards the ultimate goal of their efforts, a Co-operative Commonwealth for Ireland.

The best people renounce all for one goal, the eternal fame of mortals; but most people stuff themselves like cattle.

If you take the creation of music and the creation of your own life values as your overall goal, then living becomes a musical process.

What had begun as a movement to free all black people from racist oppression became a movement with its primary goal the establishment of black male patriarchy.

Potentially he could be. He scored the goal four years ago in France against Argentina that was extraordinary.

To live for some future goal is shallow. It's the sides of the mountain that sustain life, not the top.

My back to the goal, physically fighting off defenders, trying to bang my goals in, every week I have to do the business for this club. That's the life of a striker.

And the goal really is to make the audience laugh, to bring them some joy.

My goal was always to be recognized as a good actor but no one was interested in that, simply because society just wants to warm towards your appearance. This is the great blemish of society.

The Bush administration also was not straightforward about the intelligence it had, releasing tenuous information that fit its goal of attacking Iraq. I feel deceived.

Composers, like authors, have a lot in common. Our main goal is to connect with the listener emotionally.

If you consider that a typical Central American consumer earns only a small fraction of an average American worker's wages, it becomes clear that CAFTA's true goal is not to the increase U.S. exports.

But if you believe in Christ and that your main goal with your life is supposed to be to honor Him and do His will, then you don't have as much pressure as someone who bases all their happiness on whether they're a movie star.

Music is my main goal, but I'm not going to rush a record out. There are so many actors who have come out with albums these days. I don't want to do it because it's the thing to do. I want to wait until the time is right.