Joel David Hamkins's user avatar
Joel David Hamkins's user avatar
Joel David Hamkins's user avatar
Joel David Hamkins
  • Member for 14 years, 4 months
  • Last seen this week
135 votes
43 answers
37k views

What are the most attractive Turing undecidable problems in mathematics?

93 votes
5 answers
9k views

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

90 votes
3 answers
13k views

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

86 votes
4 answers
10k views

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

80 votes
5 answers
6k views

How do the compact Hausdorff topologies sit in the lattice of all topologies on a set?

77 votes
9 answers
6k views

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

76 votes
6 answers
9k views

Which graphs are Cayley graphs?

76 votes
4 answers
8k views

Who first characterized the real numbers as the unique complete ordered field?

74 votes
11 answers
26k views

Does War have infinite expected length?

60 votes
8 answers
6k views

Is the ultraproduct concept fundamentally category-theoretic?

56 votes
6 answers
6k views

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

54 votes
1 answer
3k views

In the two-person Killing the Hydra game, what is the winning strategy?

47 votes
0 answers
2k views

Concerning proofs from the axiom of choice that ℝ³ admits surprising geometrical decompositions: Can we prove there is no Borel decomposition?

47 votes
7 answers
5k views

Is it easy to produce hard-to-color graphs?

46 votes
4 answers
4k views

Which topological spaces admit a nonstandard metric?

44 votes
4 answers
5k views

Is there a universal countable group? (a countable group containing every countable group as a subgroup)

44 votes
2 answers
4k views

Is multiplication implicitly definable from successor?

41 votes
2 answers
2k views

On the difference between two concepts of even cardinalities: Is there a model of ZF set theory in which every infinite set can be split into pairs, but not every infinite set can be cut in half?

40 votes
3 answers
2k views

What is the minimal size of a partial order that is universal for all partial orders of size n?

39 votes
9 answers
8k views

What proportion of chess positions that one can set up on the board, using a legal collection of pieces, can actually arise in a legal chess game?

38 votes
3 answers
3k views

Can one show that the real field is not interpretable in the complex field without the axiom of choice?

37 votes
2 answers
3k views

Is there any superstable configuration in the game of life?

36 votes
2 answers
2k views

What is the fewest number of points you must delete from $\mathbb{R}^3$ to make it not simply connected?

36 votes
8 answers
2k views

Does the truth of any statement of real matrix algebra stabilize in sufficiently high dimensions?

34 votes
5 answers
1k views

Does the exact pair phenomenon for partial orders occur in your area of mathematics?

32 votes
9 answers
5k views

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.?

32 votes
2 answers
2k views

Does Fermat's last theorem hold in the ordinals?

32 votes
3 answers
2k views

Is the hierarchy of relative geometric constructibility by straightedge and compass a dense order?

32 votes
2 answers
1k views

What is the logical status of the sentence combining the ideas of Löb and Rosser, "this sentence is provable before any proof of its negation"?

31 votes
2 answers
2k views

Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?