It's well known how the mathematicians and engineers at Bletchley Park changed the course of the war, but much less has been told about the revolution which was required to defeat the V1 bomb. The low altitude and relatively high speed of the V1 meant that standard AA guns were not capable of hitting it in with sufficient reliability. Automated, electromechanical gun laying systems and 'predictors' had been known since the 1930s but these were cumbersome and couldn't be produced in sufficient quantity.
The invention and breakthrough improvements in radar allowed aircraft to be detected electronically, all that was needed was a 'box' to connect the radar to an AA gun.
The solution was to develop an analogue computer which used stored electrical energy to represent the position and velocity of the approaching aircraft. Electronic filters were used to sort the signal (due to the motion of the craft) from the noise which arose throughout the circuitry. This filtered signal was then used to steer a gun with unprecedented accuracy.
Although this is just an electrical circuit, the principles behind its design were revolutionary. Many of the big names(*) in control theory, electronics and information theory were involved its design. They invented new techniques, but also capitalised on academic research and were able to deliver a working system in time to save countless lives.
Why is this relevant today? Well, the publication of their work after the war started the modern electronics industry. Their defining principle was that a good design begins with a mathematical analysis of the problem. Although the variables are now stored digitally and the filters are implemented as C code, the principles would still be familiar to a 1940s control engineer.
The availability of sensors and the complexity of the processes we're trying to optimise today is orders of magnitude greater than 70 years ago - but the same steps of analysis, modelling and design are just as relevant today. And the services of people who understand analogue signals and differential equations are needed more than ever.
Cambridge Consultants is one of the largest employers of mathematicians in the area - they're employed to develop the fundamental principles behind ground breaking software. This enables game changing IP to be embedded in products and keep them ahead in the marketplace for many years.
(*) Nyquist, Bode, Nichols, Wiener and Shannon just to name just a few