January 09, 2017 Monday
Bedtime Story
John von Neumann's 9-point Summary of Mathematics
John von Neumann then continued on with his elucidation of
mathematics.
6. Then Kurt Gödel showed that you cannot prove the consistency of
a system within the system itself, and that any sufficiently powerful systems
of axioms will produce an incomplete system, and so Hilbert’s program was
abandoned.
I have not dealt with this aspect of mathematics yet and hope to
elaborate on it in some future night.
7. Gödel proved that the axiom of choice and the continuum
hypothesis were consistent with the other axioms of the set theory, which meant
they could be used to prove results.
Though we have dealt with the Cantor’s continuum hypothesis and
the infamous axiom of choice, I have not discussed the role and contribution of
Kurt Gödel on these subjects.
Kurt Gödel is considered the greatest logician along with
Aristotle and Gottlob Frege.
John von Neumann was one of the few who recognized this genius in
this man who was probably too sick mentally (and physically) to take care of
himself.
It was von Neumann who used his influence over Oswald Veblen to
get Gödel out of Europe that was on the road to perdition.
Veblen as you would know helped to organize and set up the
Institute for Advanced Studies in Princeton along with Abraham Flexner.
8. Although mathematics is derived from empirical observations, it
is capable of generating specialized topics that go far beyond the visibly real
world, guided only by aesthetic criteria similar to other forms of art.
9. However, there is always the danger of straying too far from
the real world and becoming irrelevant sophistry.
With these nine points, von Neumann summarizes the story of
mathematics insisting that it bestrides the universe between empirical and
logical.
I am sorry once again that I digressed, but who can afford to
ignore John von Neumann’s perspective of mathematics.
In fact, I would insist that you go back and once again read these
9 points to get an eagle-eye view of mathematics.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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