Nothing is Everything

This is it. This is the last part of the much-loved story of mathematics.  Well, it finally made its finale in front of my eyes. The series triumphed in the later periods of their timeline. How do I say goodbye to this? Well, for starters, let’s begin with truth. The truth that for so many years, mathematicians are completely interested with space and time they were so dedicated to find answers of challenging problems.

We’re done learning the past. The histories from different portals of different continents in our planet, we’ve already rummaged through the treasure and knowledge they brought. We already managed to uncover secrets and revealed unknown leverage from both the East side of Earth and in Europe that brought us more answers and unlocking more questions to better understand the world we’re living in and the worlds beyond. Let me give you the last set of better understanding how the real mechanism of mathematics works. It’s not just us or our world. It is all about the nothingness in everything and infinity in the unknown.

In the start of modern mathematics, mathematicians strived to get credits for unsolved problems.  Or so I thought. There’s boundless energy for mathematicians to surpass greater breakthroughs. Meet David Hilbert who posed a threat to all of mankind. Just kidding.  He was famous for posing 23 unsolved problems at the beginning of the 20^th century. Think of him as a visionary and as someone who presented these 23 challenges on the 2^nd International Congress on 8^th of August in the year 1900’s.

The first problem was solved by Georg Cantor’s Continuum hypothesis. The question of if there is a transfinite number between that of a denumerable set and the numbers of the continuum was answered by Gödel and Cohen in their solution to the Continuum hypothesis to the effect that the answer depends on the particular version of set theory assumed. For the second problem, it states the compatibility of the arithmetical axioms. Gödel's incompleteness theorem indicated that it is cannot be proven that the axioms of logic are consistent in the sense that any formal system interesting enough to formulate its own consistency can prove its own consistency if it is inconsistent. Think of the phrase, ‘I always tell a lie.” And yes, some of his problems are still not answered.

There were other important mathematicians that ‘were’ and that ‘could have been’ able to provide bigger justifications to satisfy curious ideas somewhere in the film. I’m sure Albert Einstein was mentioned by Mr. Du Sautoy. And oh, I’m amazed by this Mr. Yuri Matiyasevich who became known worldwide in 1970 when he completed the last missing step in the "negative solution" of Hilbert's tenth problem by adding in the Fibonacci sequence. Yes my darlings, he shared that giant feat alongside Martin Davis, Hilary Putman and Julia Robinson herself. I realized what I’m doing for 17 years and asked, “What the fudge am I doing with my life?” At such a young age of 22, this handsome man was able to complete a long-running set of solutions. They’re really brilliant people. Who could’ve thought that it would actually take four of them to determine the solvability of a Diophantus equation? A single problem was finally scratched out of the list.

But there’s one case I should put into rest. That of Poincaré’s Chaos Theory. But I don’t really meant the theory or Henri Poincaré himself.  This is about the Poincaré conjecture and the man who provides proof for its statement which is, “Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.” The man is not your usual mathematician who would battle or rival his own brilliant kind of people to step into fame and gain credentials and money. This man, for your pleasure and assurance, is your, let’s say, humble kind of person. I called him humble since he turned down honorable recognitions given to him. He in turn is likely to have been more contented with giving contributions, another enormous challenge completed, than taking all that publicity and large amounts of money. Few people nowadays have the courage to do such regrettable action. I mean, it could have provided all his needs and wants but look at how he chose to keep off from the eyes of the world. He did all he could, his best I’m sure, and yet curious were his actions of not accepting glory. I salute this man. The world would need the likes of him. Those that would be passionately working out the tricks, every detail and mess, the what’s, the what if’s and all the rest of infinite questions. Those who would take nothing in return. Those who have willing hearts and minds to do their own thing. You wouldn’t mind knowing his name now but I gave you in greatest respect, Grigori Perelman.

And yet sometimes, too few became rare and rarity seems a myth as though they’re exceptionally unreal. But what’s real and unreal anyway? I guess it would depend one way or another. And before I forget, I had a wonderful time travelling back in time with Marcus. So much enthusiasm and love for the sake of mathematics were evident in his works. Until the next mathematical journey, way to go infinity! The last installation is seriously technical but hey, it’s the perfect way to cap all of the series. While we were busy looking into what’s already here and there, some are cracking codes in a parallel universe. Thanks Math! I finally get to know you and it was more than nice to meet you. There’s this one last quote that left me thinking, though.

You can still prove something existed even though you couldn’t construct it explicitly