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Re: Landau letter, Re: Mathematica as a New Approach...

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  • Subject: [mg127911] Re: Landau letter, Re: Mathematica as a New Approach...
  • From: "djmpark" <djmpark at comcast.net>
  • Date: Fri, 31 Aug 2012 04:00:26 -0400 (EDT)
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It's like the battle between the sexes! What would life be without it?

But here is a challenge for those who might want to think of how we could
bring Mathematica to bear on the question of the nature of mathematics.

Chapter 1, Arithmetic, in John Stillwell's book "Numbers and Geometry" is
devoted to the natural numbers, the counting process, proof by finite
descent, infinite ascent, definition or proof by induction, and material on
linear integer equations, primes and divisors. It seemed to me that his
treatment is a pretty solid core introduction to what mathematics is about.

Who could turn this into a Mathematica notebook that would teach the basic
ideas? I claim that the natural numbers arise from a PHYSICAL counting
process but infinite ascent and induction require ABSTRACTION and that is
where mathematicians especially come in. It takes both.

So who (if you agree with that) could demonstrate the idea in a notebook in
a clear and convincing manner? It would have to show why it was necessary
and how we transitioned from the physical limitations of a computer to the
abstract results and yet could still use the computer to do mathematics and
proofs.


David Park
djmpark at comcast.net 
http://home.comcast.net/~djmpark/index.html 

  

From: Alexei Boulbitch [mailto:Alexei.Boulbitch at iee.lu] 


<< Original Discussion
It is also clear from history that mathematics developed from very concrete
foundations in things like counting and measurement. It is incomprehensibl e
to me that many mathematicians wish to deny this, preferring to believe in
Platonic fairy tales. 


<< Alexei
Let me just point out that the origin of this interesting and passionate
discussion was the question of what should be the content and tools of the
mathematical education for students in non-mathematical specialities at
present, observing that since long computers have become the reality of our
world.



Best, Alexei




Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu<mailto:alexei.boulbitch at iee.lu>




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