February 10, 2017 Friday
Bedtime Story
Hilbert Sets Out to Straighten Up Mathematics
David Hilbert wished to leave no stone unturned in mathematics and
sought nothing less than complete perfection in mathematics.
For this, he threw the gauntlet and declared that certain goals needed
to be achieved.
These goals or the ideals went by the name of Hilbert’s Program and
were essentially as follows:
Total
formalization of mathematics:
This meant that mathematics will have its own formal language with
very precise and well defined rules.
Completeness:
This would mean that anything and everything in mathematics could
be proved by its own well defined rules which were set up in the above
mentioned formal system.
Consistency:
By this, Hilbert meant that using the rigid rules and formal
language of mathematics, no contradictions should be obtained in mathematics.
For this Hilbert made a special appeal to stick to “finitistic”
reasoning to countable mathematics.
Hilbert was quite certain that if he could do away with Cantor’s troublesome
infinities, he could cleanse the glorious mathematics with all kinds of
paradoxes and inconsistencies.
Conservation:
Hilbert hoped that the proofs that had been obtained about “real
objects” using “ideal objects” should be obtainable without having to resort to
using ideal objects.
Decidability:
Hilbert stated that the veracity or falsity of any mathematical
statement ought to be decided by an algorithm.
With these five goals, Hilbert set the task to straighten up
mathematics.
These goals can be summed up in 3 statements that he wrote in
1919:
“We are not speaking of arbitrariness in any sense.
Mathematics is not like a game whose tasks are determined by
arbitrarily stipulated rules.
Rather, it is a conceptual system possessing internal necessity
that can only be so and by no means otherwise.”
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.
Advertisements
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:
No comments:
Post a Comment