Vivat Libertas

We live in a dark age. It is an age where truth doesn't matter and where learning is dismissed as elitism, a world where people latch onto the words of demagogues who promise them authenticity in a world which has none. It is an age - yet another age - where we persecute groups for political power and prestige. We are on the edge of something terrible and unspoken. I am an optimist. I believe we can pull ourselves back from this edge, if we have radical political overhaul and evidence-based policy. For the latter part at least, we will need numbers. In the age where people have had enough of experts, it's going to be difficult to get people to trust numbers. In many ways, mathematical manipulation represents everything popularly presented as elitism: mathematics is abstruse and frequently inscrutable to those who haven't spent several years studying its ways. Arguments made from mathematics are dry and emotionally unavailable. Economics (and crashing the economy) ...

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...

I have a mathematical mind. To those who know me, this is no great secret. To those who don't know me, it's not something that I try to hide. I can't necessarily say that it's particularly fun, nor that it's particularly difficult. It's just how I am and I've never known anything else, so I can't compare. It's definitely useful for a hell of a lot of stuff, from analysing music and literature to doing the stuff I'm actually supposed to do. What I will say is that it's frustrating. Imagine that you speak another language pretty much natively. To an English speaker, for example, this language is abstract, unintuitive and overall difficult to understand. The language is difficult if not impossible to translate without butchering it beyond all recognition, and people think you're strange for speaking it. All the same, English and not mathematese is the current lingua franca, so you grit your teeth and get translating. Now imagine you st...

So maybe some of you are sitting down with a page of maths exercises and feeling close to tears because you're so frustrated that you can't figure out what to do. I mean, it can't just be me, right? And when, like me, you actually like maths to the point of thinking that it's beautiful, it's even more frustrating and upsetting. I have a couple of things to say about this. Firstly, unless your teachers or professors are really  mean (or just incompetent) those problems are solvable. Maybe not with the tools you have right now, maybe you might need to use old tools in a different way, but they're probably solvable. And getting hysterical usually doesn't help with doing maths - well, it doesn't help me with doing maths at any rate. Secondly, take your time. I don't know how I can stress this enough, because it's important and most people (including me) forget to do this. Obviously certain things are going to be quite straightforward and you mi...

It occurs to me that I really, really don’t mind staying up till midnight doing maths; in fact, I actually quite enjoy it. Yes, you heard me correctly – I am that strange, unnatural and perhaps slightly broken person who genuinely enjoys mathematics. I’ve talked about it before, I think, how I consider maths an elegant and beautiful language to work with. But more than that, it’s just…well…it’s fun. I find it a very natural language to work in, and I enjoy learning more and more of its grammar and vocabulary every day. It calms me down when I need to relax and fires me up when I see something new. More than anything, it just makes sense: from the relatively simple equation F=m dv/dt to the beauty that is Euler’s relation, it’s elegant and precise and, to my mind, deeply intuitive.

"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 ...