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Ansatz?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101045] Ansatz?
  • From: AES <siegman at stanford.edu>
  • Date: Mon, 22 Jun 2009 04:23:03 -0400 (EDT)
  • Organization: Stanford University

Wolfram MathWorld says:

   An ansatz is an assumed form for a mathematical statement 
   that is not based on any underlying theory or principle.

   SEE ALSO: Conjecture, Hypothesis, Principle, Proposition

Somewhere I've picked up the idea that "ansatz" can also be used to 
indicate the "form" or the "approach" -- more specifically, something 
like the choice of coordinates and variables and equations -- the 
"geometry and notation" so to speak -- in which one sets up a problem or 
a calculation.

The "underlying theory or principles" in my interpretation can be 
perfectly clear, and no "Conjectures" or "Hypotheses" need be involved.  
One is simply setting up the calculation using this ansatz, in order to 
calculate certain consequences or numerical results (a calculation which 
one, of course, carries out using Mathematica).

Is my interpretation of this term off the mark?  (Wikipedia's 
explanation of the term seems to me considerably closer to my 
understanding than to Wolfram's definition.)


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