January 12, 2017 Thursday
Bedtime Story
Who Can Possibly Think of Formalizing and Rigorously Defining Natural Numbers?
What inspired John von Neumann to construct natural numbers were
the axioms that were formulated by Peano.
In the days of Peano, mathematical logic was at its inception.
The fact that arithmetic needed to be formalized was very little
appreciated then.
Even today, if you ask any average ape and tell that about 1, 2, 3…numbers
and they will not raise a finger.
For us natural numbers are obvious numbers.
They are perfectly intuitive as it makes perfect sense to our
evolved brains that needs to count apples or a herd of sheep or babies.
And hence for us that is enough.
Not so for Peano.
For Peano, even the so called natural numbers had to be rigorously
formalized and defined.
If you recall von Neumann’s exposition of mathematics, it was
geometry that was first formalized by Euclid and remained so for centuries.
The next topic in mathematics to be taken up seriously was
mathematical analysis, first by the Chinese mathematicians Liu Hui somewhere in
260 AD and then two centuries later by Zu Chongzhi somewhere in 460s AD.
Later it was taken up with great fervous by Madhava who founded
the Kerala School of Astronomy and Mathematics in 1560 or so.
He was probably the first ape of this planet who discovered the
infinite series for the trigonometric functions of sine, cosine, tangent and
arctangent.
The infinite series which go by the name of Madhava series are
divine and most beautiful.
Take just the two following examples:
sin x = x - x3/3! + x5/5! - x7/7! + …
cos x = x - x2/2! + x4/4! - x6/6!
…
Mathematical analysis is a curious branch of mathematics that
deals both with infinitesimals (too small to be measured) and infinite series
(too vast to be contemplated).
It was only in late 1800s that attention to formalize the numbers
was given thanks to men like Hermann Grassman and Charles Sander Peirce.
Peano was another one of such men.
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.
The Madhava Series
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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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