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.

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.

To see a world in a grain of sand and heaven in a wild flower Hold infinity in the palms of your hand and eternity in an hour.

Falsehood has an infinity of combinations, but truth has only one mode of being.

Suffering is permanent, obscure and dark, And shares the nature of infinity.

To see the world in a grain of sand, and to see heaven in a wild flower, hold infinity in the palm of your hands, and eternity in an hour.

If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.

God is the tangential point between zero and infinity.

It is good a philosopher should remind himself, now and then, that he is a particle pontificating on infinity.

Yet it is in this loneliness that the deepest activities begin. It is here that you discover act without motion, labor that is profound repose, vision in obscurity, and, beyond all desire, a fulfillment whose limits extend to infinity.

I cannot help it - in spite of myself, infinity torments me.

Debauchery is perhaps an act of despair in the face of infinity.

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.

Now an infinite happiness cannot be purchased by any price less than that which is infinite in value; and infinity of merit can only result from a nature that is infinitely divine or perfect.

If the infinity of the sea may call out thus, perhaps when a man is growing old, calls come to him, too, from another infinity still darker and more deeply mysterious; and the more he is wearied by life the dearer are those calls to him.

In the case of composite colour, an infinity of systems must be obtained for maxima infinitely slight and with an infinity of interval values separating them - that is to say, the whole thickness of the sensitive layer is occupied in continuous manner by these maxima.

There is a fifth dimension, beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition.

The last proceeding of reason is to recognize that there is an infinity of things which are beyond it. There is nothing so conformable to reason as this disavowal of reason.