What does quantum physics have in common with DNA or the modern computer or nuclear deterrence? What do these concepts share with fractals or with Monte Carlo simulations? Or with quantum logic, mathematical economics, linear programming, statistics, operator theory, fluid dynamics or game theory?
Maybe I should have asked “who” they have in common rather than “what” - John von Neumann!
Von Neumann was a mathematician in the first half of the 20th century who made valuable contributions in each of the fields I have mentioned. The mathematics he developed has largely impacted many areas that affect how we do and understand life around us today.
Climate change? Yes! Investments? Yes! Nanomedicines? Yes! Economics? Yes! Your cellphone? Yes! Your computer? Yes!
Von Neumann showed us how mathematics affects much of what we take for granted in everyday life. Mathematics touches every aspect of our modern life in some way or form. Mathematics forms the framework of most fields.
Mathematics underpins all innovation in finance, science, engineering, and business. However, mathematicians are the inventors but seldom the executors or the agents of their ideas. There is a disconnect between mathematics as a science and the utilisation of mathematics in the life that surrounds us.
The electrician works out the resistance or electrical supply to the new house. A plumber works out the angle to connect a drainage pipe. The painter works out the amount of paint he needs to paint your home - all numbers-based, subject to calculations, and somewhere, at different levels, related to mathematics.
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Our mathematics hero, Von Neumann, illustrated this bridge by inventing the mathematical area known as game theory. It involves studying the best decision to make in any situation. Von Neumann proved the minimax theorem for two-player games where both players have all the information needed to make choices.
His result showed that the best strategy in such a game is where the worst-case situation has the least awful outcomes. He later extended this to games with incomplete information.
Scientists famously implemented game theory during the Cold War, where both the USA and the USSR had nuclear weapons. The game-theoretical approach to prevent use of the weaponry, was to ensure that retaliation would totally obliterate the opposing side.
This type of concrete application of mathematics is often not at all expected or even suspected. It is never clear what theory may end up solving a real-life problem, and this is precisely where the actual value of mathematics lies.
Kerstin Jordaan, Mathematics is much more than the numbers!
