March 30, 2017 Thursday
Bedtime Story
Mathematics is totally deductive.
But deductive from where?
It got to start from some place.
This starting point in mathematics are the most primitive
assumptions called the axioms.
Its axiomatic origin was giving rise to lots of flaws and
inconsistencies in mathematics that was giving men like David Hilbert
nightmares.
Anything could be flawed, but not mathematics.
That was the idea then as still many of us are led to believe so
even today.
David Hilbert was an optimist who thought that with rigor and
determination, these little flaws would be ironed out and mathematics could be
built up on solid axiomatic foundations.
Russell had tried to smoothen things out and yet while working on
his Principia he had discovered a paradox in set theory that we had discussed in
one of our bedtime stories.
Little did Hilbert know that his dreams were about to be shattered
for good by a little know man then.
On September 7, 1930 Kurt Gödel had unleashed the first hint of
his incompleteness theorems in a round table gathering of the Conference of
Epistemology.
All of my bedtime stories that I have narrated, starting from
Cantor and continuing up to Hilbert, are linked and form the basis for the
thesis that Kurt Gödel chose to work upon in 1929.
If you recall, it was the 1928 Hilbert-Ackermann book “Principles
of Mathematical Logic”, an introduction to the first-order logic where the
famous question was posed:
“Are the axioms of a formal system sufficient to derive every
statement that is true in all models of the system?”
Gödel took this question very seriously and decided to write a thesis
on it under the guidance of Hans Hahn.
In all likelihood, all his contributions to mathematics has not
given him as much recognition as the fact that he had Kurt Gödel as his
student.
Hans Han also contributed indirectly to the founding of the Vienna
Circle.
It did not take long for Gödel to make the breakthrough.
Within the year of 1929, Gödel defended his doctoral dissertation
that he called the completeness theorem.
The year following the dissertation, on November 17, 1930 the
Vienna Academy of Science published the incompleteness theorems under the
title:
“On Formally Undecidable Propositions of Principia Mathematica and
Related Systems.”
The language was German and the journal was Monatshefte für
Mathematik.
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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