July 15, 2018 Sunday
Bedtime Story
Galois Introduces the Word 'Group' into Mathematics
If you were to see Galois’ mathematical
notes, you would be appalled for to call it as undisciplined would be a
grotesque understatement.
I will try to get the image of a sample of
mathematical notes made by him in tonight’s bedtime story.
But such illegible scribbling is also a
reflection of a total mathematical genius.
Lacking the characteristic rigor and
proofs, mathematicians like Galois bound along almost on pure mathematical
instinct just like great ophthalmic surgeons are known to operate at spinal
level rather than active conscious cortical application.
What was worse than the examiners’ not
comprehending Galois’s mathematical intuition was his temper that was prone to
short outbursts and this, as you know, never is helpful in going up the ranks
of hierarchy.
The dark and almost mysterious misfortunes
almost never ceased to follow him as when he tried to publish his memoir on
equation theory, for some reason or the other, it failed to get published.
Once it was refused the publication by the
mathematician Cauchy and later when he submitted it to the Academy’s secretary
Joseph Fourier to be considered for the Grand Prix, Fourier passed away and the
memoir was lost for good.
His loss turned out to be somebody else’s
gain with Niels Henrik Abel (about whom we will know more later) and Carl
Jacobi winning the Grand Prix prize.
Despite the lost memoir, Galois published
three papers that year one of which laid the foundations for what is now known
as the Galois Theory.
I shall not go into the details of the duel
and his death interesting as it may be to many of us.
After his death, some sixty pages or so of
his work survived that had landmark ideas in mathematics and had far reaching
consequences in many field of mathematics.
Despite the lack of any kind of recognition,
or rather even active and willful ignorance of his brilliant mind, Galois
himself had no doubt regarding the importance of his work.
These are the closing lines of a letter
that he wrote to his friend dated May 29, 1832, just two days before his death
and probably aware that he was dying:
“Ask Jacobi or Gauss to publicly give their
opinion, not as to the truth, but as to the importance of these theorems.
Later there will be, I hope, some people
who will find it to their advantage to decipher all this mess.”
He would have been delighted to know that today
many great minds use his work, not only in the field of mathematics but also
mathematical physics.
His work has led to the creation of a whole
new field of abstract algebra whose application is normally universal.
Galois was the first to use the word group
in a sense that is used by the modern mathematicians and this makes him along
with others one of the founders of the group theory in algebra.
Group theory of abstract algebra has become
so vastly encompassing that the Galois Theory forms only a puny speck of the
larger edifice.
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.
The famous scribblings of Galois which made it undecipherable for even the best of the mathematicians
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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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