The Story of Maths 4: To Infinity and beyond

Now, we are on to the last episode of the BBC documentary, Story of Maths. The documentary has shown, from the very first episode down to its last one, the history of Maths, how it evolved, developed and flourished through time.

The final episode considers the unsolved mathematical problems that were faced by the great minds of the 20^th century. As mentioned, “Mathematics is about solving problems and it’s the great unsolved problems that make Maths really alive”.

In the International Congress of Mathematicians, David Hilbert, a young German Mathematician, boldly set out what he believed were the 23 most important problems for mathematicians to crack. These problems redefined the Mathematics of Modern Age.

It was George Cantor who proposed who really understood infinity. It was suggested that the infinity of fractions is much bigger than the infinity of whole numbers but later on proved that the infinities of both whole numbers and fractions have the same size. There was one problem that Cantor could not get over with for the rest of his life, the Continuum Hypothesis.

Fortunately, there was one mathematician from France who stood up for Cantor and believed that Cantor’s new mathematics of infinity was beautiful. He was considered to be the greatest mathematician France ever produced, Poincaré. Paris became the center of Mathematics and it was Poincaré who shed light to the world of Maths during this time.

In 1885, a prize was given to anyone who could establish mathematically whether the orbit would continue turning like clockwork. Poincare simplified the problem by making successive approximations to the orbit which he believes would not affect the final outcome significantly. His ideas were sophisticated enough to win him he prize. However a problem was identified and that Poincare made a mistake. His simplification didn’t work because even the small change in the conditions could affect the results. The orbits Poincaré indirectly led to what is known as the Chaos Theory.

An 18th century puzzle was presented: “Is there a route in the city which crosses each of the seven bridges only once?” It was Leonard Euler who solved the problem. He realized that we don’t really care about the distance because what really matters is how the bridges are connected together. This is the problem of the new set of geometry, the position: the problem of topology.

Topology evolved as a powerful new way of looking at shape because of Poincare. Some people refer to topology as bendy geometry.

In this last installment of the documentary, I seriously thought of how I could connect Mathematics into my course which is Communication Arts. I admit, I still wonder whether there is significance between math and communications or not. However, on second thought, Mathematics after all is communication in itself. It contains a technical language, spoken not only by a few great minds, but even us, ordinary people. And that both Math and Communications have theories as foundations of their study which of course, should be and would be put into practice.