What does Gödel's Incompleteness mean for the Working Mathematician?

From: "Bob Stewart" <bobstewart_III@xxxxxxxxxxx>
Date: 31 Jul 2005 06:37:03 -0700

As I understand, Gödel showed that within a logical system,
propositions can be formulated that are undecidable or undemonstrable
within the axioms of the system. That is, within the system, there
exist certain clear-cut statements that can neither be proved nor
disproved. Hence one cannot, using the usual methods, be certain that
the axioms will not lead to contradictions.

As a working mathematician (who is not an expert in logic), how worried
should I be that the statement that I am trying to prove is not one of
these undecidable statements?

.

Follow-Ups:
- Re: What does Gödel's Incompleteness mean for the Working Mathematician?
  - From: Bhup
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  - From: double d
- Re: What does Gödel's Incompleteness mean for the Working Mathematician?
  - From: Torkel Franzen

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