January 08, 2017 Sunday
Bedtime Story
Continuing with von Neumann's Exposition of Mathematics
Continuing with von Neumann’s exposition of mathematics, he went
on to say:
2. Standards of rigor change over time (generally in an
incremental fashion)
This reminds me of the book by Russian-American lesbian writer
Masha Gessen on Grigori Perelman who solved the soul conjecture, Thurston’s
geometrization conjecture and eventually the famed Poincaré conjecture.
It is hard to describe or even understand for an average ape like me
the extent of mathematical rigor required in converting these conjectures to
theorems.
3. Calculus became real analysis with gradually increasing rigor.
I have yet to write a story on calculus as it seems a formidable
subject.
I still have not come up with a decent way of presenting it as a
story yet it is critical that I come up with something as it seems to be
central to everything in mathematics and also in physics.
Maybe some night I will.
4. George Cantor invented a theory of sets that contained
paradoxes involving infinite sets.
We have dealt with this in great detail and I hope the paradoxes
that infinities give rise to have reached home.
Of course, it is only a paradox to us as we apes are finite
creatures in all respects who have evolved in a finite landscape having to deal
with finite objects and mates for survival and reproduction.
5. Hilbert and others tried to remove the problematic parts of the
set theory and prove that the rest was consistent (free of contradictions).
This too we had gone in good depth dealing with Zermelo-Fraenkel
Set Theory and controversial axiom of choice.
I have to discuss the Hilbert’s Program which is important as it
reflects the extreme discomfort the mathematicians were facing in the early
1900s due to the paradoxes that were springing all over.
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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