Brian Micklethwait asks:
But what about the kind of maths that really is maths, as opposed to mere arithmetic, with lots of complicated sorts of squiggles? What about infinite series, irrational numbers, non-Euclidian geometry, that kind of thing? I, sort of, vaguely, know that such things have all manner of practical and technological applications. But what are they? What practical use is the kind of maths you do at university? I hit my maths ceiling with a loud bump at school, half way through doing A levels and just when all the truly mathematical stuff got seriously started, and I never learned much even about what the practical uses of it all were, let alone how to do it.
I also get that maths has huge aesthetic appeal, and that it is worth studying and experiencing for the pure fun and the pure beauty of it all, just like the symphonies of Beethoven or the plays of Euripides.
But what are its real world applications? Please note that I am not asking how to teach maths, although I cannot of course stop people who want to comment about that doing so, and although I am interested in that also. No, here, I am specifically asking: why learn maths?
I would split the subject into two. For past a certain level, it most certainly is two entirely different disciplines. The first is pure maths. For those who like it (most definitely a subset of the population) it\’s glorious, beautiful, engaging, even thrilling. It\’s also a description of the universe as it ought to be. Any connection between results and the real world is entirely coincidental: pure mathematicians are the original "yes, that\’s all very well in practice, but is it true in theory?" people. Once you climb into the higher realms (well past A levels) the value is like that of poetry. That\’s not to say that more practically useful things don\’t come from it, of course they do, but it\’s not done for its practicality nor will anyone attempting to do it for its practicality do very well at it.
Statistics rather reverses this. Looking at it in one way it\’s rather like, yes, well, this is all very well in theory but is it true in practice? We go out and gather real world information and then examine it to see what it tells us. While we might think that x happens because of y, we actually want to find out whether that is true. Or does y happen because of x? Or do they both happen because of a? Or are they simply correlated rather than caused by any of them? And many statistical tests are designed to work out how important our result is.
There\’s two things that statistics are extremely useful for. The first is to teach you how to gamble: that\’s the root of the whole subject anyway. Seriously, it really started with people trying to work out how to win at cards and dice. Things like the Fibonacci series, which explains things as varied as the placing of petals on a flower and possibly the curling of a wave, also explain the liklihood of throwing a 4, 5 or any other number with a pair of dice. From that we derive ! and so on.
But the second thing it\’s extremely useful for is politics. The standard intro by some pantywaist who wants to steal your liberty, livelihood and freedoms is "research has shown that….". Statistics enables you to evaluate whether research actually has shown (the death rate from Ebola is 80% so yes, clamping down on movements and civil liberties during an outbreak can be justified) or not shown ("the part time pay gap for women is 40%", no, it isn\’t, that\’s comparing the wages per hour of part time women against full time men. Comparing part time women against part time men gives us 11%.) the point that the speaker is trying to make.
Which of the two you are good at, which you prefer doing, largely depends upon your mindset at the beginning. I\’m not very good at either, but I do struggle to understand the statistics side as well as I can for defending those liberties, livelihoods and freedoms from those who would steal them on spurious grounds seems to me rather important.