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Is there a analysis conjecture proven to be unprovable or a proof is non-existence?

So, is it once a math history milestone

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why two downvote – Victor Jun 28 '12 at 22:01
There is a large number of assertions of analysis that have been proved independent of ZFC. – André Nicolas Jun 28 '12 at 22:11
@AndréNicolas - Maybe you could explain what is a ZFC in your answer. – Victor Jun 28 '12 at 22:13
@Victor Google "ZFC" and click the first result, which for me is the Wikipedia page on Zermelo–Fraenkel set theory (+ Choice). This is usually assumed to be the underpinning of mathematics. If you want to worry about provability, you should probably read that page. – Dylan Moreland Jun 28 '12 at 22:15
Victor, did you mean to ask "why two upvotes"? – The Chaz 2.0 Jun 28 '12 at 22:51
up vote 4 down vote accepted

There is a large number of statements in analysis that have been proved independent of the axioms of ZFC. For a partial list, see this. A fair number of them are questions that had already been asked, and worked on seriously, long before they were proved independent.

Added: ZFC is Zermelo-Fraenkel set theory, with Axiom of Choice added. It is currently, and has been for quite a while, the standard "background theory" for most of mathematics.

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