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Topic: Is "motivation" in mathematics a fairy tale?
Replies: 4   Last Post: Apr 9, 2014 2:25 PM

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Aatu Koskensilta

Posts: 2,633
Registered: 6/28/08
Re: Is "motivation" in mathematics a fairy tale?
Posted: Apr 7, 2014 8:44 AM
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Arturo Magidin <magidin@member.ams.org> writes:

> Generalization for the sake of generalization, unification for the
> sake of unification, is worthless. Only when the generalization allows
> new insight or allows the theory to reach further, only when
> unification allows new insight or allows techniques that were
> restricted to one setting to be used in new settings (to better or new
> effects) is such generalization/unification generally deemed
> worthwhile.


Quite so. Grothendieck, for instance (as we all well know) in a
seminal display of mathematical prowess managed to simplify an 80 page
paper of Serre into over a thousand pages of abstract nonsense in
_Eléments de Géométrie Algébrique_. That this was not a surreal exercise
in deranged mathematical performance art is a perfect illustration of
what's at issue when we in mathematics speak of "motivation".

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus



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