“Some infinities are bigger than other infinities.”-John Green, The Fault in Our Stars.
In the fourth installment of The Story of Maths, mathematician
Marcus du Sautoy embarks another exquisite journey through the stories of the
mysteries revolving the unsolved problems in the world of math, the
mathematicians that asked them, and the mathematicians that attempted to find
the solutions.
Mathematician Georg Cantor stirred minds when he showed that all
infinite decimal numbers are put into a set, it would produce a bigger infinity
compared to infinite set of whole numbers and fractions. I find this cool
because whatever list can be made, a decimal number can be filled in between.
This discovery fascinated him, his fellow mathematicians, and even us that
watched the documentary. I always find the concept of infinity vast and
complicated, and now I can say that it can only be described in one word:
unimaginable.
Other mathematicians that were highlighted is the Chaos Theory
by Henri Poincaré and his “bendy geometry” that paved way to the world of 3-D;
Kurt Gödel, who revealed his incompleteness theory; Paul Cohen who
attempted to dwell on Cantor’s hypothesis and tried to prove it; and Évariste
Galois and Alexander Grothendieck focused on the hidden structures of
equations.
This fourth episode of this documentary has given me a new
concept of infinity and that not all mathematics can be easily solved through
equations and operations: it needs more than that. And that mathematics have
its own mysteries, waiting for the sleuth to unlock it.
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