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 20th century. Think
of him as a visionary and as someone who presented these 23 challenges on the 2nd
International Congress on 8th 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
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