Beauty in mathematics.
Often when reading a good maths book, the author will get to the end of an explanation of a particularly complicated proof, theorem, or idea, and mention the “beauty” of the maths involved. I always wonder what, exactly, this means. Did I miss a particularly neat diagram? Or, as seems to be the case, is mathematical beauty something buried deep: something that, perhaps, I need a PhD to get to grips with?
I used to think that it was the latter — maybe one day, after years of studying maths at its highest level, I’d suddenly gain a glimpse of some incomprehensibly deep truth and realise the incredible beauty of things which now seem boring and trivial.
Maths can be like a dense jungle — it’s hard to penetrate but you never know whom you might might.
But actually, I think you can get a glimpse of what mathematicians mean by beauty without too much effort at all. That’s what I’m going to try and convince you of in the rest of this article. Mathematics can be a bit like a dense, never-ending jungle. It can feel like you’re hacking away and away at it and never getting anywhere, but if you stop and look around yourself, every once in a while you see incredible, exotic plants and animals to marvel at — and ever so often you find large new swathes of jungle to explore.
The particular thing that I want to introduce you to, that I think is so beautiful, is something that was mentioned in passing on a television programme I was watching. I hardly knew what it meant, and I certainly had no idea how it came about, but I knew I had to find out more.
I am talking about Euler’s identity
Now you probably think I’m crazy. What’s beautiful about that? Well, I ought to warn you, I’m not alone — Mathematical Intelligencerreaders voted the identity the “most beautiful theorem in mathematics”. The physicist Richard Feynman called the formula it is derived from “one of the most remarkable, almost astounding, formulas in all of mathematics”.