February 11, 2017 Saturday
Bedtime Story
"Principles of Mathematical Logic" (1928)
In 1928 Hilbert along with Wilhelm Ackermann published a book
titled “Principles of Mathematical Logic” that became a landmark in itself.
It was the first every mathematical text that was totally based on
formalism of first-order logic often abbreviated to FOL.
It was again in this landmark book of 1928 that the
Entscheidungsproblem or the decision problem was first stated clearly.
The decision problem posed by Hilbert and Ackermann asks this
following question:
Are the axioms of a formal system sufficient to derive every
statement that is true in all models of the system?
Or in other words,
Can an algorithm be made that takes as input a statement of
first-order logic and that can come out with an answer “yes” or “no” as to
whether that statement is universally valid?
Universally validity refers to a statement or a theorem being valid
in every structure satisfying the axioms.
Does not seem to be a very pressing query, does it?
Anyway, let us leave aside this problem for a while as going into
it will lead me far astray from what I have been planning to address for a long
time.
Just as an aside, the co-author of the book “Principles of
Mathematical Logic” Wilhelm Ackermann despite being a mathematician of high
caliber never joined any university for profession.
(Nearly all serious mathematicians need universities to support
themselves.)
(In fact, it often seems to me that the role of universities is
not merely to nurture young minds but involves support and sustentation of
academic minds long after they have been groomed; for certain brilliant minds
are simply inept of surviving in the cruel world outside).
Nor did Ackermann emigrate to the United States of America which
may or may not have accepted him since the deluge of Europeans sailing to
America was huge and overwhelming.
Ackermann remained and continued to be a high school teacher till
the very end.
Remarkable!
This high school mathematics teacher is known for another feat
that was bought to the attention of this average ape by his computing friend.
Being a computer guy, he does seem to know something about
computing.
I always thought that computer science guys repair broken
computers.
Obviously I was wrong as always.
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