The Goldberg Variations is a good example of how symmetry is not just a physical property but pervades many abstract structures.
Mathematics is a place where you can do things which you can’t do in the real world.
The reason why we do maths is because it’s like poetry. It’s about patterns, and that really turned me on. It made me feel that maths was in tune with the other things I liked doing.
Its my belief that you can take everyone down a logical path if you take them slowly enough, and the trouble is that mathematical brains can get scrambled a little bit on the way. You get a bad teacher, it messes you up for the rest of the journey.
Theory is needed to tell you where to look.
Primes are the atoms of the arithmetic – the hydrogen and oxygen of the world of numbers.
The power of mathematics is often to change one thing into another, to change geometry into language.
I’m obviously attuned to pick up mathematics whenever I can see it. But in Mozart there is a lot of conscious use of mathematical symbolism and numbers in order to try and give messages.
If you can make yourself symmetrical, you’re sending out a sign that you’ve got good genes, you’ve got a good upbringing and therefore you’ll make a good mate.
When people ask me what my religion is, I say its the Arsenal.
I think science is a foreign land for many people, so I think of my role as an ambassador’s job.
The stage is like a laboratory where you can run theatrical experiments, imposing interesting conditions on the cast or story and seeing how they pan out. Each new play is like creating a tiny virtual universe enclosed by the confines of the stage.
I think my primary audience is in some sense an adult audience, because I think that will then have a knock-on effect for children.
The best mobile phone had the best mathematician. They know how to fit a huge amount of data into a small amount of space. How to do things efficiently, how to do them cleverly.
One of the most curious consequences of quantum physics is that a particle like an electron can seemingly be in more than one place at the same time until it is observed, at which point there seems to be a random choice made about where the particle is really located. Scientists currently believe that this randomness is genuine, not just caused by a lack of information. Repeat the experiment under the same conditions and you may get a different answer each time.
The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth. This.
I also fell in love with Borges. He is a mathematician’s writer. His short stories are like mathematical proofs, delicately constructed and with ideas laced together effortlessly. Each step is taken with precision and watertight logic, yet the narrative is full of surprising twists and turns.
The knowledge of what we are ignorant of seems to expand faster than our catalogue of breakthroughs.
For any scientist the real challenge is not to stay within the secure garden of the known but to venture out into the wilds of the unknown.
The first algorithm to win its creators a Nobel Prize – originally formulated by two mathematicians, David Gale and Lloyd Shapley, in 1962.