I am what is referred to in the financial community as a `Rocket Scientist'--someone from a science or engineering background who has migrated, for better or for worse, to the real world of finance. For most of us, it is for the better. Why? Because applied mathematicians have changed the face of the financial markets in recent times.
Most of the important mathematics used in financial markets dates from the 1970s. The biggest jump occurred when the US space programme was wound back. Many real rocket scientists and engineers found themselves departing NASA, for destinations ranging from the pedestrian world of supermarkets to the glitzy world of financial markets. Some of those early rocket scientists made dramatic impacts. They took the known powerful mathematics of diffusion processes, heat transfer, turbulent fluid mechanics, rocket propulsion, communication, information theory, signal processing, control engineering, etc. and applied it to modelling situations in finance, which were mathematically analogous.
The early rocket scientists solved real problems. They made money--sometimes very large amounts--for their employers. They were supplemented by non-rocket scientists and engineers. So now we use stochastic processes, partial differential equations, stochastic differential equations, measure theory, genetic algorithms, artificial neural networks, martingales, fuzzy logic, non-linear optimisation, dynamic programming, stochastic programming and so on, as our tools of trade in the financial world.
The story is one of simple problems producing very complex mathematics, involving real benefits for the financial world and for the broader community.