User Qiaochu Yuan

37 votes

2 answers

3k views

How can I define the product of two ideals categorically?

asked Feb 9, 2010 at 5:15

36 votes

3 answers

3k views

If Spec Z is like a Riemann surface, what's the analogue of integration along a contour?

asked Nov 4, 2009 at 17:52

35 votes

4 answers

4k views

How does this relationship between the Catalan numbers and SU(2) generalize?

asked Mar 5, 2010 at 17:34

35 votes

3 answers

4k views

Is every abelian group a colimit of copies of Z?

asked May 5, 2015 at 17:17

34 votes

2 answers

7k views

What is the geometric meaning of integral closure?

asked Oct 20, 2009 at 22:13

33 votes

5 answers

4k views

Is every (finite-dimensional, complex) representation of a finite group defined over the algebraic integers?

asked Oct 17, 2009 at 8:09

33 votes

7 answers

3k views

Do non-associative objects have a natural notion of representation?

asked Apr 12, 2010 at 20:14

33 votes

2 answers

2k views

What are the "correct" conventions for defining Clifford algebras?

asked Oct 28, 2014 at 23:44

32 votes

2 answers

2k views

When is there a submersion from a sphere into a sphere?

asked May 25, 2015 at 23:02

32 votes

2 answers

3k views

Do we expect that sufficiently large computable ordinals settle every question of arithmetic?

asked Oct 14, 2022 at 22:27

32 votes

3 answers

7k views

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

asked Nov 19, 2010 at 1:10

32 votes

4 answers

4k views

Modular curves of genus zero and normal forms for elliptic curves

asked Mar 4, 2010 at 0:17

31 votes

2 answers

4k views

Number theory textbook based on the absolute Galois group?

asked Feb 12, 2010 at 4:05

31 votes

2 answers

3k views

Is there a "finitary" solution to the Basel problem?

asked Dec 21, 2009 at 9:17

31 votes

8 answers

5k views

Resources for graphical languages / Penrose notation / Feynman diagrams / birdtracks?

asked May 18, 2010 at 23:29

31 votes

1 answer

4k views

For which varieties is the natural map from the Chow ring to integral cohomology an isomorphism?

asked Dec 10, 2013 at 6:36

30 votes

1 answer

2k views

Which of the proofs of the fundamental theorem of algebra can actually produce bounds on where the roots are?

asked Sep 21, 2019 at 16:32

30 votes

7 answers

4k views

When is a monic integer polynomial the characteristic polynomial of a non-negative integer matrix?

asked Nov 3, 2009 at 14:47

29 votes

3 answers

4k views

How can simple physical "proofs" of mathematical facts be made rigorous?

asked Sep 16, 2010 at 1:39

29 votes

1 answer

2k views

Is there a topological space X homeomorphic to the space of continuous functions from X to [0, 1]?

asked Mar 17, 2017 at 2:01

27 votes

8 answers

2k views

Examples of sequences whose asymptotics can't be described by elementary functions

asked Nov 8, 2010 at 10:09

26 votes

3 answers

4k views

How are these two ways of thinking about the cross product related?

asked Jul 30, 2010 at 7:13

26 votes

1 answer

1k views

From the perspective of bordism categories, where does the ring structure on Thom spectra come from?

asked Jul 9, 2014 at 17:27

25 votes

1 answer

4k views

What kind of random matrices have rapidly decaying singular values?

asked Feb 25, 2014 at 2:02

25 votes

0 answers

1k views

What, precisely, do we mean when we say that a f.d. vector space is canonically isomorphic to its double dual?

asked Sep 13, 2020 at 5:35

25 votes

4 answers

7k views

"Natural" pairings between exterior powers of a vector space and its dual

asked Jun 16, 2011 at 21:18

25 votes

5 answers

2k views

Exotic principal ideal domains

asked Feb 24, 2011 at 10:54

25 votes

8 answers

6k views

What is the "right" definition of a ring?

asked Oct 27, 2009 at 2:37

25 votes

7 answers

4k views

Can adjoint linear transformations be naturally realized as adjoint functors?

asked Oct 14, 2009 at 3:18

25 votes

7 answers

3k views

When can we prove constructively that a ring with unity has a maximal ideal?

asked Nov 28, 2009 at 6:31

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179 Questions

How can I define the product of two ideals categorically?

If Spec Z is like a Riemann surface, what's the analogue of integration along a contour?

How does this relationship between the Catalan numbers and SU(2) generalize?

Is every abelian group a colimit of copies of Z?

What is the geometric meaning of integral closure?

Is every (finite-dimensional, complex) representation of a finite group defined over the algebraic integers?

Do non-associative objects have a natural notion of representation?

What are the "correct" conventions for defining Clifford algebras?

When is there a submersion from a sphere into a sphere?

Do we expect that sufficiently large computable ordinals settle every question of arithmetic?

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

Modular curves of genus zero and normal forms for elliptic curves

Number theory textbook based on the absolute Galois group?

Is there a "finitary" solution to the Basel problem?

Resources for graphical languages / Penrose notation / Feynman diagrams / birdtracks?

For which varieties is the natural map from the Chow ring to integral cohomology an isomorphism?

Which of the proofs of the fundamental theorem of algebra can actually produce bounds on where the roots are?

When is a monic integer polynomial the characteristic polynomial of a non-negative integer matrix?

How can simple physical "proofs" of mathematical facts be made rigorous?

Is there a topological space X homeomorphic to the space of continuous functions from X to [0, 1]?

Examples of sequences whose asymptotics can't be described by elementary functions

How are these two ways of thinking about the cross product related?

From the perspective of bordism categories, where does the ring structure on Thom spectra come from?

What kind of random matrices have rapidly decaying singular values?

What, precisely, do we mean when we say that a f.d. vector space is canonically isomorphic to its double dual?

"Natural" pairings between exterior powers of a vector space and its dual

Exotic principal ideal domains

What is the "right" definition of a ring?

Can adjoint linear transformations be naturally realized as adjoint functors?

When can we prove constructively that a ring with unity has a maximal ideal?