User Asaf Karagila

99 votes

Which math paper maximizes the ratio (importance)/(length)?

answered Oct 29, 2011 at 22:39

82 votes

Results from abstract algebra which look wrong (but are true)

answered Jan 20, 2023 at 9:17

69 votes

Mathematical "urban legends"

answered Jan 31, 2011 at 18:53

40 votes

Conway's lesser-known results

answered Apr 12, 2020 at 18:19

38 votes

Accepted

Linear Algebra without Choice

answered Sep 19, 2013 at 22:24

37 votes

Accepted

If someone can prove Goldbach conjecture assuming the continuum hypothesis, do we consider the conjecture proved?

answered Jan 5, 2022 at 15:26

32 votes

What are some noteworthy "mic-drop" moments in math?

answered Mar 11, 2019 at 13:49

30 votes

Accepted

How to construct a basis for the dual space of an infinite dimensional vector space?

answered Apr 25, 2017 at 14:16

30 votes

Trichotomies in mathematics

answered Feb 3, 2013 at 14:32

29 votes

What are some examples of theorem requiring highly subtle hypothesis?

answered Jun 2, 2020 at 22:11

27 votes

Accepted

Is there a theorem whose only known proof uses "$A$ or not $A$" for undecidable $A$

answered Nov 19, 2016 at 18:47

26 votes

Accepted

How much of GCH do we need to guarantee well-ordering of continuum?

answered Jul 2, 2014 at 7:44

26 votes

What are some nice uses of ultraproducts/ultrapowers?

answered Jul 21, 2023 at 9:45

23 votes

When was the continuum hypothesis born?

answered Jul 6, 2013 at 8:50

23 votes

Does ZF+AD settle the original Suslin hypothesis?

answered Sep 17, 2017 at 5:25

22 votes

Hahn's Embedding Theorem and the oldest open question in set theory

answered Apr 27, 2013 at 23:01

21 votes

Compactness of the Hilbert cube without the Axiom of Choice

answered Jan 19, 2013 at 21:54

20 votes

Accepted

Relation between the Axiom of Choice and a the existence of a hyperplane not containing a vector

answered Oct 22, 2018 at 13:52

20 votes

A better way to explain forcing?

answered Aug 21, 2020 at 7:57

20 votes

Is there an "anti-choice axiom"?

answered Feb 12, 2022 at 15:00

20 votes

Accepted

Proof/Reference to a claim about AC and definable real numbers

answered Jun 25 at 15:52

19 votes

Accepted

Is it consistent that $|[\kappa]^{<\kappa}| > \kappa$?

answered Feb 18, 2019 at 13:36

18 votes

Accepted

Does "cardinal arithmetic is well-defined" imply axiom of choice?

answered Aug 2, 2015 at 11:51

18 votes

Accepted

BCT equivalent to DC

answered Oct 3, 2020 at 12:47

18 votes

Has any open/difficult problem in ordinary mathematics been solved only/mostly by appeal to set theory?

answered Oct 26, 2020 at 9:47

18 votes

Accepted

Is the non-triviality of the algebraic dual of an infinite-dimensional vector space equivalent to the axiom of choice?

answered Oct 28, 2011 at 23:29

18 votes

Accepted

Do Measurable Cardinals Exist? (assuming ZFC)

answered Jul 8, 2013 at 21:36

18 votes

Accepted

Non continuous Linear form on $E=C([0,1],\mathbb{R})$ without AC

answered Oct 14, 2013 at 17:55

18 votes

What choice principles does "every set is in bijection with a transitive set" imply?

answered Oct 2 at 14:01

17 votes

Elementary + short + useful

answered Dec 19, 2013 at 23:10

Stack Exchange Network

305 Answers

Which math paper maximizes the ratio (importance)/(length)?

Results from abstract algebra which look wrong (but are true)

Mathematical "urban legends"

Conway's lesser-known results

Linear Algebra without Choice

If someone can prove Goldbach conjecture assuming the continuum hypothesis, do we consider the conjecture proved?

What are some noteworthy "mic-drop" moments in math?

How to construct a basis for the dual space of an infinite dimensional vector space?

Trichotomies in mathematics

What are some examples of theorem requiring highly subtle hypothesis?

Is there a theorem whose only known proof uses "$A$ or not $A$" for undecidable $A$

How much of GCH do we need to guarantee well-ordering of continuum?

What are some nice uses of ultraproducts/ultrapowers?

When was the continuum hypothesis born?

Does ZF+AD settle the original Suslin hypothesis?

Hahn's Embedding Theorem and the oldest open question in set theory

Compactness of the Hilbert cube without the Axiom of Choice

Relation between the Axiom of Choice and a the existence of a hyperplane not containing a vector

A better way to explain forcing?

Is there an "anti-choice axiom"?

Proof/Reference to a claim about AC and definable real numbers

Is it consistent that $|[\kappa]^{<\kappa}| > \kappa$?

Does "cardinal arithmetic is well-defined" imply axiom of choice?

BCT equivalent to DC

Has any open/difficult problem in ordinary mathematics been solved only/mostly by appeal to set theory?

Is the non-triviality of the algebraic dual of an infinite-dimensional vector space equivalent to the axiom of choice?

Do Measurable Cardinals Exist? (assuming ZFC)

Non continuous Linear form on $E=C([0,1],\mathbb{R})$ without AC

What choice principles does "every set is in bijection with a transitive set" imply?

Elementary + short + useful