User Joel David Hamkins

36 votes

What would remain of current mathematics without axiom of power set?

answered Jun 13, 2013 at 12:58

36 votes

Accepted

Meta$^{n{-}th}$ mathematics

answered Jun 28, 2014 at 3:26

36 votes

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Large cardinal axioms and Grothendieck universes

answered Jan 24, 2010 at 2:17

36 votes

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In model theory, does compactness easily imply completeness?

answered Dec 18, 2009 at 21:44

36 votes

Succinctly naming big numbers: ZFC versus Busy-Beaver

answered Aug 6, 2010 at 5:16

36 votes

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What is the dimension of the mathematical universe?

answered May 31, 2018 at 11:44

36 votes

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Dealing with unwanted co-authorship requests

answered Nov 24, 2017 at 2:55

35 votes

What programming language should a professional mathematician know?

answered Aug 22, 2018 at 0:08

35 votes

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How many rearrangements must fail to alter the value of a sum before you conclude that none do?

answered Aug 14, 2015 at 13:33

35 votes

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A rare property of Hausdorff spaces

answered Aug 9, 2016 at 12:10

35 votes

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Are there any undecidability results that are not known to have a diagonal argument proof?

answered Sep 6, 2023 at 18:09

35 votes

Cardinalities larger than the continuum in areas besides set theory

answered Nov 4, 2010 at 1:03

35 votes

What's the use of a complete measure?

answered Jan 12, 2010 at 17:51

35 votes

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When does collection imply replacement?

answered Jan 22, 2010 at 2:14

35 votes

How do we recognize an integer inside the rationals?

answered Mar 30, 2010 at 16:50

35 votes

What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?

answered Jul 11, 2014 at 13:21

34 votes

Explicit Hamel basis of real numbers

answered Nov 14, 2010 at 19:47

34 votes

Accepted

Nontrivial circular arguments?

answered Jan 27, 2011 at 19:04

34 votes

A search for theorems which appear to have very few, if any hypotheses

answered Feb 17, 2016 at 0:01

33 votes

Accepted

Ordering of large cardinals by cardinality

answered Sep 24, 2015 at 12:52

33 votes

The concept of duality

answered Aug 26, 2011 at 1:32

33 votes

Analogies between analogies

answered Feb 2, 2010 at 15:40

33 votes

What are some reasonable-sounding statements that are independent of ZFC?

answered Nov 23, 2009 at 18:03

33 votes

Set theory and alternative foundations

answered Dec 5, 2009 at 20:26

32 votes

Equality vs. isomorphism vs. specific isomorphism

answered May 12, 2010 at 12:23

32 votes

What are some examples of colorful language in serious mathematics papers?

answered Apr 24, 2010 at 12:34

32 votes

Accepted

Definition of Function

answered Jul 3, 2010 at 11:26

32 votes

Accepted

Axiom of Symmetry, aka Freiling's argument against CH

answered Dec 17, 2010 at 15:38

32 votes

Is the statement that every field has an algebraic closure known to be equivalent to the ultrafilter lemma?

answered Nov 20, 2010 at 12:01

32 votes

Accepted

How much of the axiom of choice do you need in mathematics?

answered Aug 11, 2023 at 1:34

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1,913 Answers

What would remain of current mathematics without axiom of power set?

Meta$^{n{-}th}$ mathematics

Large cardinal axioms and Grothendieck universes

In model theory, does compactness easily imply completeness?

Succinctly naming big numbers: ZFC versus Busy-Beaver

What is the dimension of the mathematical universe?

Dealing with unwanted co-authorship requests

What programming language should a professional mathematician know?

How many rearrangements must fail to alter the value of a sum before you conclude that none do?

A rare property of Hausdorff spaces

Are there any undecidability results that are not known to have a diagonal argument proof?

Cardinalities larger than the continuum in areas besides set theory

What's the use of a complete measure?

When does collection imply replacement?

How do we recognize an integer inside the rationals?

What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?

Explicit Hamel basis of real numbers

Nontrivial circular arguments?

A search for theorems which appear to have very few, if any hypotheses

Ordering of large cardinals by cardinality

The concept of duality

Analogies between analogies

What are some reasonable-sounding statements that are independent of ZFC?

Set theory and alternative foundations

Equality vs. isomorphism vs. specific isomorphism

What are some examples of colorful language in serious mathematics papers?

Definition of Function

Axiom of Symmetry, aka Freiling's argument against CH

Is the statement that every field has an algebraic closure known to be equivalent to the ultrafilter lemma?

How much of the axiom of choice do you need in mathematics?