Vivat Libertas

Recently I started reading What is Mathematics, Really? by Reuben Hersh , an American mathematician. It's a fascinating first look at the philosophy and practice of mathematics - what mathematicians do and our ways of explaining how we should be doing it. (These often don't match up.) I value this book for three things: firstly, its clarity. While I have a background in mathematics (well, physics really, but I like pure maths and would study it more in my spare time), my background in philosophy is rudimentary at best. This puts me at a massive disadvantage when thinking about the philosophy of mathematics. Secondly, it advocates something new and something I've been thinking about for a long time. In mathematics, three philosophies dominate: mathematical Platonism (all mathematical objects exist in an idealised, abstract form independent of time and space), intuitionism /constructivism (mathematics is an activity invented by humans rather than the discovery of funda...

I think maths is beautiful. I've been saying this since I was in my teens and I don't think I'll stop until the day I stop being able to add one and one to make two. At the same time, I understand that a lot of people find maths very abstract and difficult to make sense of. (To me, maths is pretty much concrete, so I've had to actually put effort into understanding that other people don't see the world the same way.) I also think music is beautiful. I try my hardest to keep an open mind; I frequently fail, but hey, my music taste is now pretty eclectic. Or maybe just random, if you're feeling uncharitable. Over the summer, I had to write a vacation essay. Quite unsurprisingly, I chose to work on the physics of music. Slightly more surprisingly (at least to me), my friends all thought I was insane for working on something so boring. I don't blame them; the basic physics of a simple harmonic oscillator is important, but it's not exactly the most exc...

"Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is." - Paul Erdős I can't deny it: I think maths is beautiful. At this point a lot of people with a near-phobia of maths are probably going to look at their screen like it's about to eat them. How can you find something so scarily abstract so gorgeous? How can you love it so much you're looking at studying it for another four years at university - for fun?! Equally, a lot of people who understand maths are probably slightly confused; maths is a tool. It's functional, not beautiful. Where's the beauty in numbers scribbled on a page or in calculations you make when trying to build flats or predict the growth of an economy? Well, you see, in part a lot of it relies on my weird head. I don't think in English - well, not strictly ...