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Questions
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What are the most attractive Turing undecidable problems in mathematics?

apr 7 at 4:00 Douglas Ulrich 101●6

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Does War have infinite expected length?

dec 1 at 21:21 tim 1

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Is there a dense subset of the real plane with all pairwise distances rational?

mar 5 12 at 0:47 Abdelmajid Khadari 93●5

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Which graphs are Cayley graphs?

feb 21 10 at 21:39 JSE 13.4k●33●83

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Is the sphere the only surface all of whose projections are circles? Or: Can we deduce a spherical Earth by observing that its shadows on the Moon are always circular?

dec 21 10 at 2:01 Joel David Hamkins 75.1k●7●187●343

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Can we unify addition and multiplication into one binary operation? To what extent can we find universal binary operations?

dec 3 at 13:00 Mozibur Ullah 806●1●7

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Which topological spaces admit a nonstandard metric?

jul 7 at 22:46 HenrikRüping 5,319●5●27

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Can the symmetric groups on sets of different cardinalities be isomorphic?

apr 23 12 at 13:56 Andreas Blass 32.9k●4●54●109

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Is every sigma-algebra the Borel algebra of a topology?

feb 9 12 at 8:38 Jochen Wengenroth 1,534●1●13

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How many groups of size at most n are there? What is the asymptotic growth rate? And what of rings, fields, graphs, partial orders, etc.?

apr 14 10 at 14:38 Michael Lugo 8,385●2●21●48

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