Nature is written in mathematical language.
One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.
I write rhymes with addition and algebra, mental geometry.
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.
There might be a hidden structure in pi that we simply haven't discovered.
Music is what mathematics does on a Saturday night.
One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
My big thesis is that although the world looks messy and chaotic, if you translate it into the world of numbers and shapes, patterns emerge and you start to understand why things are the way they are.
As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.
Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.
As a child it was clear to me that in some sense math was in the world around us. I became fascinated by what this means. When you look at the shape of the sun and the moon, they're circles, so every time you see a circular thing, there's pi embedded in it.
There are a lot of very strong connections with music and mathematics. They both can work in patterns and sequences and repetitions.
Music is a science, in many ways it's mathematical.
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
The mind is complicated and you can't trace the roots of its processes, but there is something about mathematical and algorithmic patterns that I like to recognize in things.
Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.
Anybody can find infinite Mandelbrot figures in his navel.
The mathematician's patterns, like the painter's or the poet's, must be beautiful.
A mathematician, like a painter or a poet, is a maker of patterns.
Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.
