November 11, 2016 Friday
Bedtime Story
David Hilbert Redefines the Axioms of Euclid
David Hilbert Redefines the Axioms of Euclid
His peers and the mathematicians who followed him regard his work
on equations also known as the finiteness theorem as supreme.
Not being a mathematician myself, it is hard for me to understand
it and hence virtually impossible to explain it.
That is why mathematics summons the biggest challenge in writing.
Another pioneering work of his was to work on the axioms of
Euclid.
Hilbert constructed a whole new set of formal axioms overriding
those of Euclid.
The axioms of Euclid though undoubtedly a work of pure genius had their
glitches and pitfalls.
Euclid in his books Elements (they were 13 in all) constructed
quite literally a whole new world of geometry staring with basic definitions
and postulates or axioms which he pronounced as “self-evident truths”.
The Elements of Euclid were so phenomenally influential that even
as late as 1900s one was not deemed to be educated unless one had read them.
They held almost Shakespearian-like authority or supremacy both in
terms of legitimacy and elegant artistry.
Sadly enough, today most educated people are happily and I dare
say, even proudly ignorant of both Euclid and his works especially as they grow
up.
Yet, towering as Euclid was, he was not infallible.
One of the first to challenge him was once again a German
mathematician by the name of Moritz Pasch.
He called upon the mathematicians to bring about a greater
grounding of the assumptions made by Euclid with even more precise and
primitive notions and axioms.
Yes, primitive (meaning more fundamental)!
Hilbert taking a cue from Pasch went a step further and stated
that the axioms of Euclid could not be taken as self-evident truths.
His point was that Euclid axioms were strongly based on human
intuition specially the notions of point, line, plane and other such
fundamental concepts.
Hilbert rather stressed more upon their relationships.
In his work, Hilbert once again listed out all the undefined
concepts of Euclid such as point, line, plane, lying on, between-ness,
congruence both of points and lines and so on.
Hilbert attempted to unify the axioms of both the plane and solid
geometry into one.
This whole exercise is viewed as transformation to the modern
axiomatic method.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night and my fellow cousin ape.
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, may I
suggest this large collection of Kids Songs:
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