Art, Mathematics, and Beauty

I was sorting and filing some old papers yesterday when I came across a bunch to do with the Riemann Hypothesis. I read some of them again, for what reason I do not know. On the surface, it seemed like covering old ground for no purpose. I lost myself in them anyway.

I noticed connections I had not seen before. I worked out a few equations with question marks beside them. Since last looking at the papers, I studied basic complex analysis more thoroughly than I had before. That helped my understanding too.

I am a little surprised I can do any mathematics at all. I suppose my yearly treks into mathematics blows some of dust off the bottle. What does surprise me most is that I still lose myself in a piece of mathematics and that I still find it beautiful. I mean beautiful such as fine art in a great museum.

The best trick with any piece of mathematics no matter how elementary is finding the beauty in it. Once one feels the beauty one gets the odd sense that one cannot easily discriminate whether the author who originated it discovered it or created it. The question gnaws and nags. The beauty, however, embraces no matter what.

Let us say you think Van Gogh’s Starry Night is a beautiful painting. I do not get it. Over the years, I pass the painting in the museum, yet it does not touch me. One day when I am blue and forlorn, idly walking through the museum, I stop before the painting. It touches me; tears well in my eyes. It touches me ever as much as you once did.

Let us say I think Euclid’s proof that there are an infinite number of prime numbers is beautiful. I explain the proof to you. It leaves you cold and wondering about my sincerity when it comes to discussing beauty. One day you are blue. You remember me fondly, quirks and all. You take up Euclid’s proof one more time because of me. It touches you; tears well in your eyes.

You cannot have art without mathematics, nor mathematics without art. They are part of the imagination, our beautiful imagination, existing in an inexplicable universe of beauty that sometimes touches us at the most unexpected moments.