Philosophy introduces us to
infinity: infinity of ideas, infinity of questions, and infinity of answers. It
entices us to indulge into the world of the unknown...into the world of
infinity. Faith, on the other hand, shows us that God is infinite. The laws of this world are inapplicable to
Him for He’s the only abstract thing that’s tangible, and His love is the only
one that lasts forever. Mathematics, one
of the building blocks of human life, also exhibits infinity and explores the
land of the unexplained.
From
the frontiers of space, Marc du Sautoy now brings us to the infinity and
beyond. The story starts off with the Hilbert’s 23 problems. These 23 problems
became the stars that guided the mathematics to the Promise land, and the same
problems that had saved the world. Georg Cantor was one of the geniuses that
had stepped onto the world of infinity. He discovered the infinity of whole
numbers, as well as unending list of fractions. One of his legends was the
Continuum Hypothesis, which explores on the possibility of different infinities
and their sizes. Henri Poncaire was also puzzled by these infinities. As he was
struggling to solve the mystery at hand, Poncaire has unintentionally unearthed
another masterpiece: the Chaos theory. Topology was then established by Leonard
Euler. Two of the greatest theorems on the logic and philosophy of mathematics,
generalized as the Incompleteness theorem, were discovered by Kurt Godel. The first Incompleteness
Theorem tackles that mathematical
concepts are true, but there are also those that cannot be proven despite the
assumed validity. The second theorem supports that the consistency of such
concepts cannot be established.
Just
like philosophy, mathematics also believes that answers must not silence
questions; they must stir up curiosity and hunger for proof. The mathematician
that had claimed this was Paul Cohen, who stated that there are different
mathematical questions, and a question may be answered a dozen, a thousand, or
a million times. But who would’ve
thought that women back then also rocked the world of mathematics? Julia
Roberts, the formulator of the Robinsons Hypothesis, did rock mathematics well.
Robinsons solved Hilbert’s 10th
problem. Hilton’s problem teased mathematicians to discover a solution composed
of integers that would solve the Diophantine equations. Julia Robinsons, along with colleagues,
sufficed this question, not by providing the integral solution, but by proving
that such solution does not exist at all. A group of French mathematicians,
called Nicolas Bourbaki, had also contributed to the infinity of mathematics.
Another great mathematician discussed in the story had focused on the
structures of mathematics, and believed that breaking down a concept to its
basic units are essential to understanding the patterns of mathematics.
In
biology, cell is the structure of life. Prime numbers, on the other hand, are
the building blocks of mathematics. Riemann’s Hypothesis dwells on the distribution
of prime numbers. And it is with this hypothesis that the narrator himself,
Marcus du Sautoy, fell deeply in love with mathematics.
This
last installment of the Story of Maths was indeed the best one. Truly, the
different facades of mathematics were shown, from it being the universal
language up to being the gate to infinity and beyond. With mathematics,
confusions are cleared, and the world becomes more concrete. This I guess is
the essence of mathematics.
May the words of Hilbert saying “We must know.
We will know.” keep the fire burning. J
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