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From: jim stasheff <jds@math.upenn.edu>
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Subject: Re: fundamental theorem of algebra
Date: Sat, 01 Apr 2006 09:59:36 -0500
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Yet the one that is hard
to see is easy to prove, while the one that is easy to see is hard to
prove.

Ain't that the truth
or as Rene Thom once remarked about one of his assertions
Very easy to see, very had to prove

jim


Vaughan Pratt wrote:
[...]
>
> These questions are probably more appropriate for a philosophy of
> mathematics list than this one.  What makes FTAlg such an interesting
> case study for those with something at stake in such questions is that
> the tensions here are so extreme.  The final result (FTAlg) is not at
> all obvious, whereas the lemma it rests on, whether it be that |P(z)|
> attains its minimum, or that circles around a hole don't retract, or the
> intermediate value theorem, or the existence of a root for a real
> polynomial of odd degree, seems self-evident.  Yet the one that is hard
> to see is easy to prove, while the one that is easy to see is hard to
> prove.
>
> If seeing is believing, what is proof?  In the real world, when
> something is easy to see it is up to the opposition to demonstrate that
> it is nonetheless false.  How did mathematics evolve to play by a
> different rule book?
>
> Vaughan Pratt
>