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 drenched in mathematics.

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.

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.

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)