September
08, 2017 Friday
Bedtime
Story
What made Gottlob Frege Question the Foundation of
And
if the great Euclid could be doubted then so could the work of lesser mortals.
With
Euclid under question, the very foundations of the mathematicians began to be
analyzed and from this frenzied activity arose a new breed of mathematicians
that went by the name of logicians.
Logicians
were mathematicians who began to question the veracity of logic in mathematics
and how to set it right if it was flawed.
Gottlob
Frege was perhaps the first among this breed who not surprisingly went largely
ignored during his life time.
Most
likely other mathematicians never understood what he was trying.
Today
I wish to use this opportunity to explore and understand the mind of this
little known mathematician.
What
really made him question mathematics and its foundations in 1870s?
Was
it that he was then studying the world’s most prestigious mathematical center
Göttingen and Jena?
Was
it that one of his mentors was Ernst Abbe who along with Otto Schott and Carl
Zeiss laid the foundations of modern optics?
Keep
in mind that Gottlob Frege came much before Giuseppe Peano, Bertrand Russell,
Kurt Gödel or Alfred Tarski.
What
made him to even think that logic lies at the bottom of mathematics and it is
from logic that mathematics arises?
I
do not have a good answer for the questions that I ask myself.
But
perhaps it was the open and questioning atmosphere of Göttingen and Jena, along
with development of Non-Euclidean geometry that perhaps gave him the feeling
that something is not very proper about the foundations of mathematics.
He
perhaps also noted that Aristotelian logic was so cut off from Euclid’s basic
theorems and simple statements of number theory.
Even
a number theory statement such that are infinite number of primes did not seem
to have any connection with Aristotelian logic.
He
perhaps must have wondered in his solitude that how come two things (Euclidean
geometry and Aristotelian logic) so strongly based on logic and reason are so
disconnected.
All
this perhaps motivated him to try out and derive genuine logical principles of
inference such that in derivation of mathematical proofs no need would arise to
resort to intuition.
If
there had to be an intuition, it had to stated earnestly at the very onset and
kept aloof as axioms.
After
that, all proofs would be derived logically step wise without any gaps.
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.
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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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