August 11, 2018 Saturday
Bedtime Story
Galois's Paper Failed to Impress his Peers
In comparison with Gödel, Galois was highly
unfortunate because no one around him, even the best of the minds, was able to
grasp his work.
He failed to grasp the attention of his
peers that he rightfully deserved.
Moreover, the paper was Galois was a very
difficult one, much like the Gödel’s incompleteness theorems though Gödel was
fortunate in that he was surrounded with dazzling mathematical minds including
John von Neumann who immediately grasped the significance of the work and
exclaimed “It’s all over”.
If what I am trying to explain to you about
Galois goes over your head, you need not take it to your heart for Galois’
paper that was finally published in 1846 by Joseph Liouville made little sense
for his own mathematical contemporaries; those men who did mathematics day and
night for a living and out of love for it.
Even Liouville who himself published the
paper and praised it lavishly for its originality completely failed to grasp
the group-theoretic basis of it.
Serious mathematicians such as Cayley in
England, Kronecker and Dedekind in Germany who were the European stalwarts of
mathematics completely failed to appreciate the genius of Galois in spite of
being aware of his work.
It was only in 1880s and 1890s when
mathematical text books written by Eugen Netto and Heinrich Weber (both
Germans) gave their due respect to Galois’ work that his work came to know to
the wider audience both in the continent and across the Atlantic.
So now let us jointly try to understand
Galois’ work.
Let me break down the problem of
understanding Galois Theory in some simpler smaller problems and questions,
something in the lines of ‘divide and conquer’ technique used both in military
warfare/politics as well as phacoemulsification method of cataract surgery.
What does group of any sort has to do with
solvability or rather non-solvability of quintic or higher degree polynomials
in terms of radicals?
If the Abel-Ruffini theorem makes it clear
that quintic or higher degree polynomials have no solutions in radicals, then
what is further left to discuss or tackle?
I think I had given you a hint of the small
gap that was still left behind which to most apes would not be of much
consequence but it certainly did bother Galois.
It turns out that there are some quintics
or higher polynomials that do have a solution.
At this point we need to go back and read
what Abel philosophized about any mathematical problem.
Abel rightly pointed out (to the top class
mathematical brains who indulge themselves in the frontiers of unknown math)
that any mathematical question or problem (such as a possible proof of Riemann
Hypothesis) should be posed not merely to arrive at its solution but also in a
fashion that would suggest whether arriving at its solution is at all possible.
We shall attack this problem of Galois
Theory in the nights to come.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
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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