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

*To*: mathgroup at smc.vnet.net*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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <7061851.89395.1346314334093.JavaMail.root@m06>

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>