The tricky, unanswered questions.

“Mathematics is about solving problems and it’s the great unsolved problems that make maths really alive”. This is the very first stamtent Marcus du Sautoy mentioned in the final episode, To Infnity and Beyond. It considered the mathematical problems that are still unsolved.

Marcus first explained everything about infinity and he talked about Georg Cantor who somewhat discovered and understand the concepts of infinity. Cantor showed that infinity could be understandable. He considered the infinite set of whole numbers and compared them to the smaller sets of numbers and showed that these two infinite sets can have the same size because it is possible to pair them up. Then, fractions are considered where an infinite number of fractions between any of the two whole numbers. He said that the infinity of the fractions is much bigger than the infinity of the whole numbers. Cantor showed that there were different infinities, some bigger than others, including the decimals. However, he was still unable to solve the problem: Is there an infinity sitting between the smaller infinity of all the fractions and the larger infinity of the decimals? He only believed that his is not possible. This is considered as the first problem that is still unsolved. Uh, that was very tricky.

After that, Marcus went to a place where there were seven bridges built in there.  The trick is when you have to pass each of the seven bridges only once. This one is also tricky because I have experienced solving the same problem but in a different manner. That was when our Math1 teacher told us to draw a certain figure in such a way that each points in the picture is connected only once and you’ll get back to what point you started. The distance doesn't matter but what matters is that how the points are connected with each other, same thing as the bridges.

Then, here comes David Hilbert where he explained that equations could be constructed from a finite number of building blocks like sets. However, he could not just construct those sets he was saying, he just simply said it existed. This is also similar to our assignment in which we have to explain if this statement is either true or false: I always lie. Well, this is also very tricky because the statement could be false or true but we all know that it exists.

Honestly, these are the only points in the episode that really struck me. I haven’t focused more on the other details of the story. Although the people mentioned like Paul Cohen and Julia Robinson were also still amazing because of their questions which they cannot answer and prove. I have noticed (or just in my opinion), this episode is the most serious episode among series. I haven’t paid that much attention to the whole story, sadly. But still, I learned a lot of things! Since this is the last episode, I can definitely say that the series really opened my eyes about the stories behind mathematics. Cool! *smiles*.