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

learnmaths?

Well?

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.

I think you miss off the land which is in between.

There’s applied mathematics which describes the real world – and they do ask does this really fit the world (and if it doesn’t there’s something wrong). This uses the tools of pure mathematics to do it.

Then in my area there’s the mathematics of computer science. This has massive practical impact, from trying to show things are secure, calculating how time or space requirements of an algorithm increase with input to cryptography and cryptanalysis which help keep our credit card details secure from eavesdroppers (but not from the corruption of someone on the other end).

Its not pure or statistics there (although there’s also theoretical computer science which is really a specialised subset of pure maths)

Engineering is almost all maths based. If you’re crap at maths, you’re gonna have to work damned hard to get through an engineering degree. And surprisingly, I have found myself doing engineering calculations in my career.

Didn’t Asimov write that someone who didn’t comprehend maths probably shouldn’t be classed as human?

On the other hand, I’m still trying to get to grips with this opposable thumb thing so what do I know about it?

One of the most mystifying things about the universe is that it can be described mathematically at all. There’s nothing “as it ought to be” about it. It’s the way it is.

I’d also disagree about the split between pure and applied, and see it more as a conveyor belt from today’s blue sky research to tomorrow’s commonplace. (G. H. Hardy said, “I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” Now, of course, his ideas are used every time the little lock symbol lights up in your browser.)

Incredible as it may sound, a cocky Richard Feynman also once asked what good pure maths was. In reply a colleague at Los Alamos gave him a contour integration problem – which he was unable to solve.

Once you climb into the higher realms (well past A levels)One could make a sarcastic comment about the current A level syllabus here.

What practical use is the kind of maths you do at university?Other have mentioned areas like engineering and cryptography. I would add weather/climate prediction, seismic studies (e.g. finding oil), computer games, web search engines, medicine, finance, agriculture and forrestry, pharma and biotech, chemical industry, telecoms, energy research (e.g. fusion), semiconductors, etc – the list is huge.

pj: that was Robert Heinlein (or more accurately, his character Lazarus Long): “Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.”

I have an MSc in telecomms and microwave engineering. We built a GHz transistor amp in stripline, but that was about the extent of the actual metal-bashing we did. The rest was lecture-based, and while the mathematical content was not desperately advanced (certainly less than in my physics degree) it was pervasive. My research work at university level was concerned with implementation of wireless LANs (i.e. WiFi), which were in their infancy at that point. This involved maths, and nothing BUT maths. I didn’t build anything – this was all in simulation. In order to simulate the RF environment and the wireless LAN itself, I was using Gaussian white noise, convolutional codes, Viterbi decoders, alpha trackers, Kalman filters, Fourier analysis, you name it. All densely mathematical, and mostly simulated in hand-coded C++. As a sideline, I was also doing a bit of cryptography and number theory.

There is not a single discipline in the hard sciences or engineering at the level of actual research that is not

drenchedin mathematics.“There is not a single discipline in the hard sciences or engineering at the level of actual research that is not drenched in mathematics.” Quite: it is the language we speak.

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