Paul Siegel's user avatar
Paul Siegel's user avatar
Paul Siegel's user avatar
Paul Siegel
  • Member for 14 years, 1 month
  • Last seen this week
249 votes
16 answers
67k views

Why worry about the axiom of choice?

228 votes
9 answers
24k views

John Nash's Mathematical Legacy

136 votes
9 answers
19k views

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

114 votes
36 answers
30k views

Quick proofs of hard theorems

100 votes
6 answers
11k views

Is there an analogue of curvature in algebraic geometry?

73 votes
3 answers
3k views

Can analysis detect torsion in cohomology?

69 votes
7 answers
14k views

The main theorems of category theory and their applications

61 votes
14 answers
11k views

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

52 votes
1 answer
16k views

Atiyah's May 2018 paper on the 6-sphere

51 votes
4 answers
5k views

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

48 votes
4 answers
11k views

Central limit theorem via maximal entropy

39 votes
6 answers
4k views

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

37 votes
4 answers
3k views

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

36 votes
2 answers
5k views

Smooth homotopy theory

35 votes
10 answers
8k views

Some questions about scalar curvature

33 votes
1 answer
3k views

Is there a common genesis for ADE classifications?

31 votes
2 answers
5k views

A question about "Zariski dense" arguments

30 votes
4 answers
4k views

Elementary applications of Krein-Milman

30 votes
6 answers
3k views

Can distribution theory be developed Riemann-free?

25 votes
1 answer
927 views

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

24 votes
3 answers
3k views

Does elliptic regularity guarantee analytic solutions?

24 votes
5 answers
5k views

Curvature and Parallel Transport

24 votes
2 answers
2k views

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

23 votes
1 answer
1k views

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

22 votes
5 answers
2k views

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

22 votes
9 answers
1k views

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

22 votes
5 answers
7k views

The Jacobi Identity for the Poisson Bracket

20 votes
4 answers
3k views

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

18 votes
2 answers
3k views

Mayer-Vietoris implies Excision

18 votes
2 answers
3k views

A question about the proof of Mostow rigidity