Re: Historical CAS question

From: Martin Johansen (mfag_at_online.no)
Date: 01/23/05

  • Next message: Robert Israel: "Re: Historical CAS question" 
    Date: Sun, 23 Jan 2005 02:26:39 +0100

    Good question

    Mathematics, being the science of measurement, is about reducing a
    complicated task into mans comprehension, i.e. somthing that can be written
    down on a piece of paper and comprehended all at once.

    A golden example of this is the story of Gauss who as a child reduced
    1+2+3+...+100 to 50*101 using reason instead of automation, which the other
    students in his class did.

    Today, Gauss would not achieve this. Another student would have been thought
    how to use Maple and the computer would do the calculation for him. All the
    students would laugh at Gauss who obviously overcomplicated things.

    But, the problem is, Gauss' solution leads the way to infinite sums, which
    the computer cannot do.

    So my conclusion is, a CAS is unnecessary or damaging for mathematicians
    because it does not inspire reasoning, which is easily more powerfull than
    any CAS.

    For mathematics, use pen and paper, and for *unavoidably* repetetive tasks
    use a CAS, e.g. if you final answer is 5^log(2) and you only need an
    approximation.

    I know assembly-line workers may not agree, but they were not in the context
    of the question, right?

     - Martin Johansen

  • Next message: Robert Israel: "Re: Historical CAS question"