Well beauty is a very interesting thing, and a form of beauty that is important to me is mathematical beauty… that’s a rather austere form of aesthetic pleasure. But those of us who work in that area and speak that language can recognize it and agree about it

And we found in theoretical physics, that the fundamental laws of nature are always mathematically beautiful. In fact if you got some ugly equations almost certainly you haven’t got it right and you should think again.

So, beauty is the key to unlocking the secrets of the physical world.

Interviewer: And what are the qualities or properties, how do you describe whats beautiful about a mathematical equation?

Well its very hard, of course to describe any form of beauty, and sometimes you have to perceive it.

And its more difficult with mathematics because you have to be able to speak the language.

It’s a bit like saying, this is a wonderful Icelandic poem… but if I don’t understand Icelandic I wont get to grips with it.

So, mathematical beauty is connected with first of all everything being elegant and economic. You don’t write a great sprawling equation that takes half a page to write down.

It’s very concise.

Just perhaps a line with only a few symbols in it, but it turns out that it is also very deep, so that when you explore its consequences you find this very simple looking thing, implies this or implies that, all sorts of surprising and unexpected things. And if it a successful part of mathematical physics, of course, it would imply all sorts of phenomena happening in the world.

And that’s what we mean by mathematical beauty.

Its very hard in everyday language to get to a closer description on that .

What is striking, I think, is that those of us who happen to speak that sort of language, can agree about mathematical beauty. In fact, I suspect we agree rather more readily on mathematical beauty than, say, painters do about artistic beauty.

Transcribed from a radio interview
- John Polkinghorne on Speaking on Faith, NPR