Stack Exchange

Paul Siegel

New York

http://www.math.columbia.edu/~siegel

I am a data scientist studying the geometry and dynamics of social networks at Brandwatch .

Formerly: I got a PhD in math at Penn State in operator algebras; my thesis involved applications of K-theory for operator algebras to geometry and topology. I spent 3 years as a postdoc at Columbia University.

I have a math blog , but I don't write for it nearly often enough.

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Top Questions
225 votes

John Nash's Mathematical Legacy

riemannian-geometry big-list game-theory asked May 24 '15 at 15:58
mathoverflow.net

203 votes

Why worry about the axiom of choice?

lo.logic set-theory axiom-of-choice asked Apr 29 '10 at 2:57
mathoverflow.net

120 votes

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

dg.differential-geometry ds.dynamical-systems projective-geometry sturm-liouville-theory asked Sep 8 '10 at 22:12
mathoverflow.net

109 votes

Quick proofs of hard theorems

soft-question big-list alternative-proof asked May 16 '10 at 19:11
mathoverflow.net

92 votes

Is there an analogue of curvature in algebraic geometry?

dg.differential-geometry mg.metric-geometry ag.algebraic-geometry asked Mar 25 '10 at 14:07
mathoverflow.net

67 votes

Can analysis detect torsion in cohomology?

differential-topology asked Apr 25 '10 at 3:17
mathoverflow.net

61 votes

The main theorems of category theory and their applications

ct.category-theory big-list asked Dec 14 '11 at 16:50
mathoverflow.net

58 votes

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

3-manifolds open-problem big-list open-problems-list gt.geometric-topology asked Jul 17 '10 at 16:50
mathoverflow.net

50 votes

Atiyah's May 2018 paper on the 6-sphere

dg.differential-geometry asked Jul 1 '18 at 23:05
mathoverflow.net

43 votes

Is there a naive proof that $x - \frac{x^3}{3!} + \frac{x^5}{5!} - \ldots$ has period $2\pi$?

calculus sequences-and-series asked May 29 '18 at 19:26
math.stackexchange.com

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Top Answers
127
Why should one still teach Riemann integration?
mathoverflow.net

69
Replication crisis in mathematics
mathoverflow.net

64
Why is the tensor product important when we already have direct and semidirect products?
math.stackexchange.com

64
Quick proofs of hard theorems
mathoverflow.net

58
What do modern-day analysts actually do?
math.stackexchange.com

57
What are the most misleading alternate definitions in taught mathematics?
mathoverflow.net

56
On which regions can Green's theorem not be applied?
mathoverflow.net

53
What is your favorite isomorphism?
mathoverflow.net

50
When and how is it appropriate for an undergraduate to email a professor out of the blue?
mathoverflow.net

48
What is the significance of non-commutative geometry in mathematics?
mathoverflow.net

48
Any real contribution of functional analysis to quantum theory as a branch of physics?
mathoverflow.net

43
Are there examples of non-orientable manifolds in nature?
mathoverflow.net

42
Motivation for and history of pseudo-differential operators
mathoverflow.net

42
What are the uses of the homotopy groups of spheres?
mathoverflow.net

41
Mind-blowing mathematics experiments
math.stackexchange.com

41
Intuitive explanation for the Atiyah-Singer index theorem
mathoverflow.net

37
How are mathematicians taught to write with such an expository style?
math.stackexchange.com

35
How do I convince my students that the choice of variable of integration is irrelevant?
math.stackexchange.com

32
Why have mathematicians used differential equations to model nature instead of difference equations
mathoverflow.net

31
Should computer code be included within publications that present numerical results?
mathoverflow.net

30
When is something too big to be a set?
mathoverflow.net

30
Example of a manifold which is not a homogeneous space of any Lie group
mathoverflow.net

29
Why higher category theory?
mathoverflow.net

29
Is there a nice application of category theory to functional/complex/harmonic analysis?
mathoverflow.net

26
Analysis from a categorical perspective
mathoverflow.net

26
What problem in pure mathematics required solution techniques from the widest range of math sub-disciplines?
mathoverflow.net

25
'Category-theory'-free areas of pure math, 'category-theory'-loaded areas of applied math
mathoverflow.net

25
Classical geometric interpretation of spinors
mathoverflow.net

24
List of proofs where existence through probabilistic method has not been constructivised
mathoverflow.net

24
Category Theory usage in Algebraic Topology
math.stackexchange.com

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