Story of Math Part 4_Ong

To Infinity and Beyond

            It is already the last episode of the movie The Story of Maths. As an ender, Prof. Marcus du Sautoy focused on the 23 mathematical problems. At the International Congress of Mathematics held in Paris, David Hilbert put forth 23 unsolved problems – which was generally reckoned the most successful and deeply considered compilation of open problems every to be produced by a single mathematician.

These 23 problems ranged greatly in topic and precision. One of the problems showed in the movie was to understand infinity. This is where George Cantor comes in. Cantor showed that two different infinite sets can be equal because one element from one set can be matched with another set’s element. He also showed that some infinite sets are greater than others, such as the fraction infinite set. Cantor established the Continuum Hypothesis. This hypothesis proposes that if you are given a line with an infinite set of points marked out on it, then just two things can happen: either the set is countable, or it has many elements as the whole line. There is no third infinity between them. In 1950’s another mathematician tried to solve the Continuum Hypothesis. His name was Paul Cohen. He found that there existed two equally consistent mathematical worlds. In one world the Hypothesis was true and there did not exist such a set. Yet there existed a mutually exclusive but equally consistent mathematical proof that Hypothesis was false and there was such a set. 

Topology or bendy geometry was also discussed in this last episode. It is geometry of location where the distance is not what matters but how things like bridges or routes are interconnected. I am amazed by the fact that one mathematician was able to compile these sort of problems. Each of the problems has its own importance in the mathematical world. I know that Hilbert was expecting during his time that one day all these problems would each have their own solutions. As what Hilbert said – “We must know, we will know.” May all mathematicians and scientists out there have the bravery and courage to stand up to the challenges they face. And one day, be able to achieve what they wanted to do – to search for answers.