To Infinity and Beyond (Story of Maths 4)

The fourth and last episode of BBC Story of Math was entitled To Infinity and Beyond. The video episode started out with mention of “twenty-three then unsolved” mathematical problems formulated by David Hilbert. Throughout the video, it was discussed how different mathematicians through generations tried to solve these problems and how they came up with solutions to these problems raised.
First of which was Georg Cantor who dealt with the concept of infinity. He measured how the infinity of fractions could actually be bigger than the infinity of real numbers. This statement seemed strange for me. I thought how does one measure something infinite? How does one know that one infinite is bigger than the other? Shouldn’t it be immeasurable? The concept of infinity is as huge and broad as infinity itself. I think it is a very complicated thing to discuss and even in the video I wasn’t able to fully grasp and understand the concept of infinity. I think that it is actually the nature of infinity. If people were able to grasp it that easily, if people could understand this in an instant, then it would defeats the purpose of being infinite. For example, scientists and astronomers claimed that the universe is so diverse, no one could ever note the exact width and breadth of the solar system. It is the nearest example of infinity that I could think of. And it is not known to us how complicated the universe is.
However, in Cantor’s search for answers about the concept of infinity, there was one hanging question he couldn’t answer: Is there an infinity sitting between the smaller infinity of all the fractions and the larger infinity of the decimals? The search for this question’s answer ended up with the formulation of the Continuum Theory. This only proves that in mathematics a question may be left unanswered but it will probably open new doors for new possibilities and new concepts, just exactly how philosophy works. Mathematics by itself resembles infinity.
In the 1950’s though, this problem of Continuum Theory was revisited by Paul Cohen. He discovered 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. Cohen would subsequently work on Hilbert’s eighth problem, the Riemann hypothesis, although without the success of his earlier work.”