I stumbled across a Wikipedia article called Mathematical Beauty. Rather an unusual encyclopaedia entry, but in many ways ideal: to have a subject presented from an enthusiast’s viewpoint should be the starting point for any subject. Read the quotes at the beginning of the article: good perspective from some famous aficionadoes.
I studied pure mathematics as an undergraduate major, and it was greatly enjoyable. It’s a puzzle enthusiast’s joy for the solution, or the reader’s joy in elegant prose, a well-constructed plot, or a moving journey. Except that in this case, you’re seeing beauty in a ruthless, immutable truth.
The discussion of various types of beauty in maths is something that strikes a chord with me. Beauty in method is what mathematicians typically refer to as elegance; this is my most common experience of beauty. But I particularly appreciate a line of thought that draws in two seemingly unrelated strands of thought – beauty in results. Calculus is good for this. And the recently-created proof of Fermat’s Last (unsolved) Theorem – which took several years of the solver’s life – is a good illustration of the value – and capability, and necessity – of drawing in different branches of thought.
But I particularly love Euler’s Identity – which is about the most beautiful formula I’ve ever seen, for its elegance, simplicity, and deepness:
- three of the most basic constants for the price of one, all tied back to the identity.
A reminder: e is the base of the natural logarithm (ln), i is an imaginary unit on the complex number plane (the square root of -1), and pi is, well, pi (ratio of a circle's circumference to diameter). Its journey describles the semi-circumference of a unit circle from 1 to -1.
An appreciation of mathematics is the root of all science.