As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

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.

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

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 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.

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.

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 was born in Edinburgh, in Scotland, a few days after the end of the Second World War. Both my parents had left school at a very young age, unwillingly in my father's case. Yet both had deep effects on my education, my father influencing me toward measurement and mathematics, and my mother toward writing and history.

Negative gender stereotypes related to girls' education in science, technology, engineering, and mathematics begin as early as primary school and have the devastating effect of making them doubt their own potential.

The mathematics of quantum mechanics very accurately describes how our universe works.

In my family, as in most middle-class Indian families I knew when I was growing up, science and mathematics were held in awe.

The mathematics is not there till we put it there.

The beauty of string theory is that it is all about mathematics. For that, you don't need resources or labs. Just sit in your room and do the maths.

You are thinking about the music, about the mathematics of it. It's time-consuming and energy-consuming at the same time. That's why I take my time off, my family time, as inspirational. I cool off.

Studying music involves a lot of mathematics and a lot of exercises of memory. Or you've got to be able to be like somebody, to play like somebody, to play Mozart's music the way he played it and how he intended it. You've got to make it perfect, and that's not what I want to do. Although it is beautiful.

An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.

As mathematics had been my best subject at school, my parents proposed - and I accepted - studies at the University of Lund in mathematics, statistics, and economics. The choice of the latter subject is said to be due to the fact that at the age of five years, I was very fond of calculating the cost of the various cakes my mother used to bake.

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.

In terms of mathematics textbooks, why can't you have the scale of a national market? Right now, we have a Texas textbook that's different from a California textbook that's different from a Massachusetts textbook. That's very expensive.

Quantum physics is a bit of a passion of mine. It's extraordinary. There's a branch of mathematics that is based on lunacy, and that's wonderful.

I find all of my performances come down to mathematics in a sense - how do you approach the problem of this character? Sometimes I crack that problem, sometimes I don't.

I earned my Ph.D. in philosophy, and one of my specializations was the logic and mathematics of game theory. I've also got a degree in drama, so I know about stories, characterizations, plot arcs, and the like. Lots of game designers can do one or the other: I've got the skills for both.

One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory.

For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics.

I think math is a hugely creative field, because there are some very well-defined operations that you have to work within. You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols.

All mathematics is is a language that is well tuned, finely honed, to describe patterns; be it patterns in a star, which has five points that are regularly arranged, be it patterns in numbers like 2, 4, 6, 8, 10 that follow very regular progression.

In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.

Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics.