The Pursuit of Greater Knowledge

The Pursuit of Greater Knowledge

A movie review on BBC The Story of Maths: To Infinity and Beyond

            After hundreds of years of developing Mathematics and discovering more of our natural world through mathematical philosophies, we finally arrive in the current status of the number world where unsolved problems are faced head-on by twentieth century mathematicians. It seemed like the Egyptians, Babylonians, Chinese, Arabians, Leibnitz, Newton, and many other people who shaped the mathematical world have contributed enough to provide the structure for us to use in our everyday lives. However, how sure are we that they did not leave any question unanswered? In this last installment of the four-part documentary of the BBC Story of Maths, Marcus du Sautoy takes us once more a little bit back in time to explore how these most recent mathematicians tried to work out great unsolved problems that the most excellent minds may have intentionally avoided.

            David Hilbert proposed 23 unsolved mathematical problems that he felt important that it must really be solved. Later on, his agenda was approved and the task to find the answer to his first proposed problem started. Georg Cantor studied the concept of infinite numbers. He compared infinite whole numbers to the smaller set of numbers. He, then, reached a conclusion that the compared infinite sets have the same size but vary in the decimal conversion of the infinite numbers. Because of this variation in infinite decimal numbers, he found out that there are types of infinity, some bigger than the others, by showing that there is a continuous missing decimal number in the conversion as he progress with the infinity sequence. Still, there is a loophole in the solution: the possibility of an infinite set between infinite sets. This is where the Continuum Theory was born stating that there is no such set. Another problem was developed from ‘Bendy Geometry’ or the concept that says, if two shapes can be moulded to be another, then they have the same topology, in the two-dimensional sense. The problem in this discipline is the identification of shapes in a three-dimensional universe. Grigori Perelman gave answer to that question. He looked at the discipline in another mathematical point of view and thus, he found ways that 3D can be manipulated in higher dimensions.

            We now know that mathematics is a universal language, a language enabling everyone to team up to find truths in our natural world proven for hundreds of years already. David Hilbert believed that too. But an active member of the “Vienna Circle” has disproved that idea. Kurt Gödel showed that the consistency of mathematics is impossible to prove and thus, there is always the unknown as an integral part of mathematics.

            As the documentary reached an ending, the learning gets more entertaining maybe because, as it gets closer to the modern math, I, as a student, can relate more to the concepts and/or ideas presented. More issues were formed; more discoveries were found. One problem may have conflicting answers and certain answers solve some theorems. Together, with everything else in the world, we move forward. There are still more unsolved problems out there and it only takes one step to start the journey to find the solution, to seek the truth, behind the unknown. It may not be easy but just one step, one step to start the pursuit of knowledge to infinity and beyond.