Re: if using Mathematica to solve an algebraic problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg108999] Re: if using Mathematica to solve an algebraic problem*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Fri, 9 Apr 2010 03:34:55 -0400 (EDT)

On 4/8/10 at 8:03 AM, dave at removedbailey.co.uk (David Bailey) wrote: >I also think that if Mathematica had been available to me back then, >I would have felt it was a bit like an addictive substance - very >interesting in small doses, but also terribly dangerous. There would >have always been the possibility of becoming skilled in answering >questions through Mathematica, rather than actually learning the >subject! While I think I understand the concern you express here, I still wonder. If one becomes very skilled at using Mathematica to solve problems correctly wouldn't there have to be some corresponding gain in understanding of how the same problems would be solved without Mathematica? The point I am trying to get at is areas Mathematica fails or shows limitations invariably require understanding of details of the problem and computer arithmetic. It seems becoming highly skilled at getting correct results from Mathematica requires mastery of these details to a large degree. And it also seems understanding those details are exactly what is required to solve the problem without Mathematica. I wonder if it is really possible to become highly skilled at getting good results from Mathematica without also learning the subject.