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Re: Ansatz?

• To: mathgroup at smc.vnet.net
• Subject: [mg101071] Re: Ansatz?
• From: "M.Roellig" <markus.roellig at googlemail.com>
• Date: Tue, 23 Jun 2009 07:06:05 -0400 (EDT)
• References: <h1nf0q$91h$1@smc.vnet.net>

Hi,

> 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.

I would say, that this is the common understanding of ansatz in
science (at least for a native german speaker). An example would be the
german word Loesungsansatz, meaning the initial choice of how to approach
(and solve) a given problem,
e.g. the starting point of a mathematical proof or the set of initial
assumptions.

> 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
>

So, to assume something without any prior derivation could be an
ansatz, but
usually an ansatz would be based on some reasonable assumptions or
additional
knowledge, so "not based on ANY underlying theory or principle" sounds
too
much like a crystal ball.

Cheers,

Markus

• Follow-Ups:
  • Re: Re: Ansatz?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>