Talk:Hilbert's third problem

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History

I've heard (more than once) that in some form Hilbert's third problem was solved "in a negative time" -- that a counter-example (perhaps, not exactly to what Hilbert had asked?), was constructed two years before 1900. Can someone clarify? --Burivykh (talk) 19:16, 21 March 2010 (UTC)[reply]

"stronger question"

In discussion of Hilbert's original question, the article refers to it as a "stronger question". That phrase doesn't quite make sense to me. I understand strength of statements -- statement A is stronger than statement B if A implies B but B does not imply A.

The original question is about a small subset of what is covered by the final published question. A "yes" answer to the original question would have been a weaker statement than a "yes" to the final question. But a "no" answer to the original question would of course imply a "no" to the final question, making it a stronger statement (which we now know to be correct).

Does the strength of a question depend on knowing the answer? Does the mathematical mainstream use the concept of strength of questions? If not I think we should re-phrase. Thundermaker (talk) 15:14, 28 September 2010 (UTC)[reply]

The Axiom of Choice

I think these are very important facts that are not mentioned in the article: a) Dehn's solution depends on the AC. b) There are other solutions that do NOT depend on the AC, so c) The answer to the problem does NOT depend on the AC. --98.176.25.65 (talk) 00:09, 1 November 2010 (UTC)[reply]

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