User Joel David Hamkins

131 votes

43 answers

36k views

What are the most attractive Turing undecidable problems in mathematics?

asked Jan 12, 2010 at 15:24

93 votes

5 answers

9k views

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

asked Mar 23, 2010 at 17:34

90 votes

3 answers

13k views

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

asked Feb 7, 2012 at 20:40

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?

asked Sep 17, 2010 at 18:02

76 votes

6 answers

9k views

Which graphs are Cayley graphs?

asked Feb 9, 2010 at 23:14

76 votes

5 answers

5k views

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

asked Feb 19, 2010 at 21:09

73 votes

11 answers

25k views

Does War have infinite expected length?

asked Jan 12, 2010 at 4:58

73 votes

9 answers

6k views

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

asked Mar 5, 2011 at 15:35

73 votes

4 answers

7k views

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

asked Jun 13, 2020 at 19:51

60 votes

8 answers

5k views

Is the ultraproduct concept fundamentally category-theoretic?

asked Jan 9, 2010 at 22:12

56 votes

6 answers

5k views

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

asked Jan 25, 2010 at 16:06

53 votes

1 answer

3k views

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

asked May 10, 2020 at 20:40

48 votes

7 answers

5k views

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

asked May 30, 2014 at 13:26

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?

asked Apr 9, 2012 at 20:32

46 votes

4 answers

4k views

Which topological spaces admit a nonstandard metric?

asked Jan 6, 2010 at 2:19

44 votes

4 answers

5k views

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

asked Jun 21, 2010 at 21:24

44 votes

2 answers

4k views

Is multiplication implicitly definable from successor?

asked Jul 9, 2022 at 12:35

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?

asked Jul 4, 2011 at 12:20

40 votes

3 answers

1k views

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

asked May 25, 2010 at 13:55

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?

asked Jul 30, 2013 at 3:10

37 votes

2 answers

3k views

Is there any superstable configuration in the game of life?

asked Jun 4, 2013 at 0:58

36 votes

8 answers

2k views

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

asked Aug 2, 2010 at 1:00

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?

asked Aug 31, 2015 at 21:33

36 votes

2 answers

3k views

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

asked Jul 13, 2021 at 13:27

33 votes

5 answers

1k views

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

asked Apr 20, 2010 at 18:23

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.?

asked Apr 13, 2010 at 21:57

32 votes

2 answers

2k views

Does Fermat's last theorem hold in the ordinals?

asked Dec 4, 2013 at 18:31

32 votes

3 answers

2k views

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

asked Nov 28, 2021 at 10:42

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"?

asked Aug 12, 2022 at 15:10

31 votes

3 answers

3k views

Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?

asked Jun 13, 2010 at 19:00

Stack Exchange Network

94 Questions

What are the most attractive Turing undecidable problems in mathematics?

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

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

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?

Which graphs are Cayley graphs?

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

Does War have infinite expected length?

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

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

Is the ultraproduct concept fundamentally category-theoretic?

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

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

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

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

Which topological spaces admit a nonstandard metric?

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

Is multiplication implicitly definable from successor?

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?

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

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?

Is there any superstable configuration in the game of life?

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

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

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

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

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.?

Does Fermat's last theorem hold in the ordinals?

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

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"?

Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?