What is this thing called Mathematics?

When I was studying at London University to become an electronics engineer, most of what we were interested in was electrons. These are the teenzy weenzy negatively charged particles that whizz around the positively charged nucleus of an atom, much as the planets whizz (a lot more ponderously) around the sun to make up our solar system. And it’s when they break free of the nucleas and flow down a wire that they become what we call electricity.


But how to study them when there was no way that we could see them? Mathematics!

In my entire three years at university, I never got to see an electron, but boy, did we build mathematical models of how they would perform under various conditions. We also had mathematical models for light waves and light particles (yes, light and electrons are both, or either, of those things depending on which mathematical model you used).

The maths in those days was pretty complicated, but now I know we were taking baby steps. From the earliest of times, mathematical formulae have been developed to represent everything in physics from the minutest particles to the universe up there. Einstein was a post office clerk turned mathematical genius. He predicted, mathematically, that the closer to the speed of light an object travelled the slower it’s time would pass. Years later this was proved in a laboratory by mounting a radioactive particle in the centre of a disk and a similar particle on the edge, then spinning the disk very fast and measuring the rates of radioactive decay of each particle. The one on the outside decayed more slowly than the one at the centre and the results coincided with Einstein’s equations.

He also wrote the famous formula:Emc2

Which suggested (audaciously) that mass (that is physical matter) could be turned into an incredible amount of energy, because energy (E) is equal to the mass (m) times the square of the speed of light. And as the square of the speed of light is 89,875,517,873,681 kilometres a second, that would be one hell of a big bang! Well, as the inhabitants of Hiroshima and Nagasaki found out, it was a hell of a big bang.

Today, this same equation drives nuclear power stations in which radioactive elements decay by exchanging mass for energy. The energy heats the water in the boilers and the steam drives the turbines that produce the electricity (well, I guess that depends upon Eskom).

Physicists during and since Einstein’s time have been trying to build one mathematical model to account for the universe, gravity and time (the big picture) together with the invisibly small particles (or waves) that are the building blocks of everything that we see and touch. This is an entirely mathematical exploration, but some of the predictions (such as black holes) get verified by increasingly sophisticated observation of the universe whilst others (such as anti-matter) by smashing ultra high speed particles together at CERN, the massive underground particle accelarator which straddles the French and Swiss borders.

Here’s an example. In 1964, Peter Higgs and his colleagues demonstrated that if their mathematical model was correct, there must be a particle that carried so much energy that it had never been observed. They predicted it’s energy and mass (which we know are interchangeable because of the above formula). Only by 2012, did CERN build enough power to reach those energy levels and lo and behold, they spotted the so called Higgs Boson. It had the predicted energy and mass!

All from a set of mathematical formulae which could only be solved if the particle existed.

So what is this thing called Mathematics?




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