The
last episode for Story of Maths was more on the unsolved puzzles of math, which
is a collection of questions by David Hilbert. He had 23 problems, each was
still unsolved during his time, and he challenged the future mathematicians to
solve it one by one.
The first problem was solved by George Cantor, who lived
in East Germany. He was the first mathematician to fully understand infinity,
which was amazing, because until now I find it hard to believe that a number
such as infinity exists. It was cool the way he showed how to pair up the
infinite number of fractions with the infinite set of whole numbers.
Apparently, there are infinite infinities, each having a somewhat different
size. A problem he had thought was whether there were infinities sitting
between two other sets of infinities.
The next mathematician discussed solved how 3 heavenly
bodies could move in a stable orbit, so that he could receive the prize from
the king of Sweden who asked the problem. However, before publication, as
mistake was found in his work. This mistake was important for creating the
chaos theory, which is currently part of the 20th century
mathematics.
I got interested in the next problem about the 7 bridges,
because it was more of a puzzle than a problem. Leonard Euler proved that it
was not possible to answer the problem, which kind of left me quite
disappointed, because I was looking forward to the answer. This lead to the study
of topology, which can also be called ‘bendy geometry’, since it states that if
one object can be morphed into another without cutting it, they are
topologically the same. It’s a really interesting thing to know about, because
I do want to know how a bagel can be the same as a tea cup.
David Hilbert was an interesting mathematician, and
sometimes referred to as the most charismatic mathematician of his time. What
intrigued me was his problem. He was able to prove that there is a finite set
of equations, but he cannot somehow construct it. Hilbert was a very
interesting mathematician; a proof of this is when he collected his favorite
problems which math has not solved yet during his time. They became somewhat a
foundation of mathematics, and so many mathematicians have been dedicating
their lives to answer one of the 23 puzzles.
Another interesting mathematician was Kurt Godel, who was
somewhat odd. During his time, he loved to stay in cafes, pretty much like what
we do. Here, in his discussions with the Vienna circle, he stated on how he
wanted to solve Hilbert’s 2nd problem, but instead he proved he
opposite of it. There can be mathematical problems which are true, but cannot
be proved. It was like the sentence: I always tell a lie, wherein you can say
it is true but you cannot prove it. It somewhat made him feel blue.
Due to the raging Nazi wars, a lot of European
mathematicians fled Europe and came to America, where the Institute for
Advanced Study was waiting for them. Here, a lot of famous mathematicians
thrived, and one of those was Albert Einstein himself. Kurt Godel also went to
the institute, and he became good friends with Einstein. Soon, Kurt Goedel gave
into depression. During those times, a younger American mathematician was making his
way to the top.
Paul Cohen was young when he first loved math. At the age
of 22, he was able to find a solution for Hilbert’s first problem; that there
could be a mathematics where the continuum hypothesis was true, and the other
mathematics where the continuum hypothesis was false. No one believed him that
much, but after Kurt Goedel said yes, his answer was correct, he received a lot
of fame and money. I can’t believe being a mathematician could actually make
you earn money. Sometimes, I wonder what it would be like going to the same
institute as they had. It would’ve been fun and at the same time, could induce
a lot of pressure due to the presence of the many highly intellectual people.
It really made me quite proud that there were female
mathematicians who also rocked the mathematics world. One of them was Julia
Robinson, who from a young age showed full potential in mathematics. She stayed
in the University of California, found her partner, married and settled onto
Hilbert’s 10th problem. Apparently, it was solved by Yuri
Matiyasevich, who was 22 when he found the answer. It was sweet of him to thank
Julia with all his heart, since she was his inspiration for solving the
problem.
Nicholas Bourbaki was another math star, for he had
numerous books which were used as foundations. Apparently, he was not one
person, but rather a group of mathematics lead by Andre Weil, who was a great
Russian mathematician.
At the end of the movie, I learned that out of all the 23
problems, the 8th one has not been solved yet: the Riemann’s
hypothesis. Maybe one day, I would be the one to solve it. Maybe.
All in all, the Story of Maths as a wonderful journey
throughout the mathematical world. It was amazing how a lot of people
contributed to form foundations for the subject, and how they just exchanged
problems to be solved. It helped be somewhat appreciate math a lot more. I will
be missing Du Sautoy though, because of how witty he is and how he was able to
make me watch everything without getting bored. The adventures of math that we
have gone through proved how hard yet enjoyable it is, despite the fact that it
sometimes caused depression and paranoia. Still, I grew to appreciate math
more, and hopefully I will continue on to appreciating it, or maybe be able to
solve problems that have never been solved before.
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