I guess there are two kinds of beauty; Natural and Interpreted.
Our universe is, for many of us, beautiful by its very nature. From the movement of stars and the geology of our planet, to the complexities of Darwinian evolution, we can find beauty anywhere we choose to look.
Beauty however, does not have form. It doesn't exist as something distinct. A mountain is a mountain in the same way a star simply shines. Whilst each have mass, volume and density, their beauty indexes remain elusive.
All interpreted beauty, such as music, painting and literature is an attempt to make this notion real. In painting a landscape for example, the artist attempts to capture this elusive quality and restrain it within a wooden frame, so that others may see it and grasp the mind boggling nature of our universe.
Brilliant as we are, we still lack the capacity to wholly comprehend the universe. Therefore we rely on our artists to describe it metaphorically, and our scientists to describe it physically.
For me, the works of the scientist and artist converge most clearly in the field of mathematics. Now,the extent of my mathematical education reaches no further than GCSE (B), and slightly advanced sociology statistics, or 'how to manipulate the truth'. I like maths, but I've chosen a different path for my life. So, this is what Bertrand Russel had to say about it,
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."
I like recurring decimals. 3/10 = 3 and a third. The third = .3333333333... ad infinitum.
I like the maths of orbit using Newtonian assumptions.
I like how prime numbers seem random.
And of course, who could not like PI. The most beautiful of numbers.
Many see divine intervention in mathematics. I see patterns and beauty. No God. Our minds are build to see patterns, trends and significances. The temptation to see God in this most irrational of numbers gets the better of many.
Just like Maximillian Cohen in the film PI. Here's a great clip from an even greater film;