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Re: Uniform design

  • To: mathgroup at
  • Subject: [mg48334] Re: Uniform design
  • From: Paul Abbott <paul at>
  • Date: Tue, 25 May 2004 07:16:49 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <c8kd99$msp$> <> <c8ptuj$kpi$>
  • Sender: owner-wri-mathgroup at

In article <c8ptuj$kpi$1 at>,
 Andrzej Kozlowski <akoz at> wrote:

> One way to view the history of mathematics, and along with it the 
> history of "mathematical tools"(of which Mathematica is just one) is as 
> an unending struggle between two view points. There are various ways to 
> look at it, but one that particularly appeals to me, is through the 
> personalities of two of the greatest figures in the history of all 
> human thought: Newton and Leibniz. Leibniz, as is well known, had a 
> great interest in logic and abstract ideas. He also wished to create 
> perfect and universal tools that would enable the most ignorant and 
> stupid persons to solve the most difficult problems. In the works of V. 
> I. Arnold:
> "On the basis of Pascal's studies and his own arguments Leibniz quite 
> rapidly developed formal analysis in the form in which we know it. That 
> is, in a form particularly suitable to teach analysis by people who do 
> not understand it to people who will never understand it. Leibniz wrote 
> 'A poor head, having subsidiary advantages,... can beat the best, just 
> as a child can draw with a ruler better than the greatest master by 
> hand."
> Newton, was of course the opposite. He did not care for generality and 
> even at first did not wish to study Euclid because (in Arnold's words): 
> "he thought it was foolish to prove things that were quite obvious". 
> But Barrow persuaded Newton to master geometry and this proved useful 
> when Newton on purpose decided to make his Principia as difficult as 
> possible, since he did not wish any "poor heads" to be able to make any 
> sense of it.
> While I do not think the designers of Mathematica had exactly the same 
> intention as Newton, I am sure they also never intended it to be used 
> the way Leibniz wished his "universal method" to be used.

To the contrary, I'm pretty sure that the designers of Mathematica, 
principally Stephen Wolfram, did intend Mathematica to be used in the 
way Leibniz proposed. One reason the student version is a "full version" 
is so that students do not run into artificial limitations imposed by 
many other software packages.

> I am also pretty sure that Newton would have liked Mathematica and Leibniz 
> most likely not. All of us are in some degree on one side and the other, as 
> one can tell from the frequency that issues like those in this posting 
> are raised on this list.

I think that they both would have liked Mathematica -- though maybe 
Leibniz would have preferred a system like Axiom with mathematics "at 
its foundation". Perhaps an interesting point for discussion is the 
design of D versus Derivative (an operator and a functional) in 
Mathematica compared to the notations developed by Leibniz and Newton.

I also believe that Euler would have _loved_ Mathematica. There was a 
nice article on this in TMJ 1(4) 1991:37-38 called "Three Excerpts from 


Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
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Crawley WA 6009                      mailto:paul at 

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