User Paul Siegel

256 votes

16 answers

71k views

Why worry about the axiom of choice?

asked Apr 29, 2010 at 2:57

228 votes

9 answers

24k views

John Nash's Mathematical Legacy

asked May 24, 2015 at 15:58

137 votes

9 answers

19k views

Is there an underlying explanation for the magical powers of the Schwarzian derivative?

asked Sep 8, 2010 at 22:12

115 votes

36 answers

31k views

Quick proofs of hard theorems

asked May 16, 2010 at 19:11

102 votes

6 answers

11k views

Is there an analogue of curvature in algebraic geometry?

asked Mar 25, 2010 at 14:07

74 votes

3 answers

4k views

Can analysis detect torsion in cohomology?

asked Apr 25, 2010 at 3:17

69 votes

7 answers

15k views

The main theorems of category theory and their applications

asked Dec 14, 2011 at 16:50

62 votes

14 answers

12k views

What are some of the big open problems in 3-manifold theory?

asked Jul 17, 2010 at 16:50

52 votes

4 answers

6k views

Does anyone know an intuitive proof of the Birkhoff ergodic theorem?

asked Jun 21, 2010 at 21:15

52 votes

4 answers

13k views

Central limit theorem via maximal entropy

asked Oct 7, 2014 at 1:38

52 votes

1 answer

17k views

Atiyah's May 2018 paper on the 6-sphere

asked Jul 1, 2018 at 23:05

39 votes

6 answers

4k views

Is the Laplacian on a manifold the limit of graph Laplacians?

asked Jun 4, 2011 at 13:35

38 votes

2 answers

6k views

Smooth homotopy theory

asked Aug 11, 2010 at 7:26

37 votes

4 answers

3k views

Why is it so hard to compute $\pi_n(S^n)$?

asked Oct 20, 2014 at 23:27

36 votes

10 answers

8k views

Some questions about scalar curvature

asked Jun 30, 2010 at 11:38

35 votes

1 answer

3k views

Is there a common genesis for ADE classifications?

asked Jul 24, 2010 at 22:04

32 votes

6 answers

3k views

Can distribution theory be developed Riemann-free?

asked Aug 9, 2011 at 7:41

32 votes

2 answers

5k views

A question about "Zariski dense" arguments

asked Aug 23, 2014 at 14:43

30 votes

4 answers

4k views

Elementary applications of Krein-Milman

asked May 19, 2012 at 20:57

25 votes

1 answer

964 views

Do free higher homotopy classes of compact Riemannian manifolds have preferred representatives?

asked Aug 11, 2010 at 17:32

24 votes

5 answers

2k views

When is the time evolution of a Hamiltonian system described by the geodesic flow on a Riemannian manifold?

asked Oct 1, 2010 at 22:07

24 votes

3 answers

4k views

Does elliptic regularity guarantee analytic solutions?

asked Jul 28, 2010 at 4:21

24 votes

5 answers

6k views

Curvature and Parallel Transport

asked Mar 2, 2010 at 11:59

24 votes

2 answers

2k views

How much of homotopy theory can be done using only finite topological spaces?

asked Jul 30, 2014 at 18:26

23 votes

1 answer

1k views

What are some geometric reasons why a Dirac operator would have a gap in its spectrum?

asked Feb 27, 2011 at 20:10

22 votes

9 answers

2k views

Why do dynamicists worry so much about differentiability hypotheses in smooth dynamics?

asked Mar 28, 2010 at 14:37

22 votes

5 answers

8k views

The Jacobi Identity for the Poisson Bracket

asked Jun 16, 2010 at 18:39

20 votes

4 answers

3k views

Is there a statistical interpretation of Green's theorem, Stokes' theorem, or the divergence theorem?

asked Feb 28, 2013 at 15:33

18 votes

2 answers

4k views

Mayer-Vietoris implies Excision

asked May 22, 2012 at 3:26

18 votes

2 answers

967 views

Is there an axiomatic characterization of the entropy of a continuous random variable?

asked Feb 18, 2017 at 23:44

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66 Questions

Why worry about the axiom of choice?

John Nash's Mathematical Legacy

Is there an underlying explanation for the magical powers of the Schwarzian derivative?

Quick proofs of hard theorems

Is there an analogue of curvature in algebraic geometry?

Can analysis detect torsion in cohomology?

The main theorems of category theory and their applications

What are some of the big open problems in 3-manifold theory?

Does anyone know an intuitive proof of the Birkhoff ergodic theorem?

Central limit theorem via maximal entropy

Atiyah's May 2018 paper on the 6-sphere

Is the Laplacian on a manifold the limit of graph Laplacians?

Smooth homotopy theory

Why is it so hard to compute $\pi_n(S^n)$?

Some questions about scalar curvature

Is there a common genesis for ADE classifications?

Can distribution theory be developed Riemann-free?

A question about "Zariski dense" arguments

Elementary applications of Krein-Milman

Do free higher homotopy classes of compact Riemannian manifolds have preferred representatives?

When is the time evolution of a Hamiltonian system described by the geodesic flow on a Riemannian manifold?

Does elliptic regularity guarantee analytic solutions?

Curvature and Parallel Transport

How much of homotopy theory can be done using only finite topological spaces?

What are some geometric reasons why a Dirac operator would have a gap in its spectrum?

Why do dynamicists worry so much about differentiability hypotheses in smooth dynamics?

The Jacobi Identity for the Poisson Bracket

Is there a statistical interpretation of Green's theorem, Stokes' theorem, or the divergence theorem?

Mayer-Vietoris implies Excision

Is there an axiomatic characterization of the entropy of a continuous random variable?