User Paul Siegel

22 votes

Penrose tilings and noncommutative geometry

answered Oct 21, 2010 at 12:33

21 votes

Abstract thought vs calculation

answered Jul 1, 2010 at 19:44

21 votes

Is there a database for tracking the dependencies of mathematical theorems?

answered Sep 8, 2016 at 18:12

21 votes

Accepted

Homotopy groups of Fredholm operators

answered Aug 19, 2014 at 17:16

21 votes

Accepted

Where does the Laplace transform come from?

answered Aug 29, 2020 at 12:14

21 votes

Question about information measurement for continuous random variable

answered Apr 5, 2022 at 1:50

21 votes

Mindset to understand category theory

answered Apr 4, 2021 at 1:18

20 votes

Why are polynomials so useful in mathematics?

answered Jun 13, 2014 at 6:53

20 votes

Accepted

Atiyah-Singer theorem-a big picture

answered May 20, 2017 at 23:42

20 votes

Accepted

Atiyah-Patodi-Singer Eta invariant and Chern-Simons form

answered Jan 7, 2012 at 6:52

19 votes

Accepted

Fundamental group of a compact manifold

answered Jan 9, 2013 at 10:05

19 votes

Theorems that are 'obvious' but hard to prove

answered Jan 9, 2011 at 16:48

19 votes

Accepted

How and why did mathematicians develop spin-manifolds in differential geometry?

answered Oct 14, 2015 at 17:49

18 votes

How we do actually compute the topological index in Atiyah-Singer?

answered Apr 21, 2013 at 15:26

16 votes

Accepted

An easy way to to explain the equivalence definitions of tangent spaces?

answered Feb 19, 2012 at 18:11

16 votes

How to quantify noncommutativity?

answered May 11, 2012 at 18:39

16 votes

How do you present a non-existence theorem?

answered Oct 27, 2011 at 23:19

16 votes

Integrals from a non-analytic point of view

answered Sep 12, 2010 at 16:18

16 votes

Accepted

Reference: Learning noncommutative geometry and C^* algebras

answered Feb 3, 2011 at 12:28

15 votes

Accepted

Alternative undergraduate analysis texts

answered May 24, 2010 at 4:55

15 votes

Accepted

A survey for various $K$-homology theories and their relationship

answered Apr 26, 2015 at 15:48

15 votes

Accepted

The principal symbol as an element in the K-theory

answered Aug 12, 2022 at 18:35

14 votes

Surprising connection between linear algebra and graph theory

answered Jul 9, 2014 at 14:21

14 votes

Applications of Atiyah-Singer using pseudodifferential operators

answered Jan 13, 2014 at 16:57

14 votes

What areas of pure mathematics research are best for a post-PhD transition to industry?

answered Apr 2, 2014 at 10:30

14 votes

Accepted

Must a manifold covered by $ S^n $ admit a metric of constant positive sectional curvature?

answered Jul 1, 2018 at 20:26

13 votes

The resolution of which conjecture/problem would advance Mathematics the most?

answered Nov 30, 2014 at 0:38

13 votes

What are some slogans that express mathematical tricks?

answered Sep 23, 2010 at 22:08

13 votes

What is the role of equivariance in the Atiyah-Singer index theorem?

answered Dec 16, 2011 at 20:55

13 votes

Accepted

Spin structures on $S^1$ and Spin cobordism

answered Nov 27, 2012 at 16:23

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161 Answers

Penrose tilings and noncommutative geometry

Abstract thought vs calculation

Is there a database for tracking the dependencies of mathematical theorems?

Homotopy groups of Fredholm operators

Where does the Laplace transform come from?

Question about information measurement for continuous random variable

Mindset to understand category theory

Why are polynomials so useful in mathematics?

Atiyah-Singer theorem-a big picture

Atiyah-Patodi-Singer Eta invariant and Chern-Simons form

Fundamental group of a compact manifold

Theorems that are 'obvious' but hard to prove

How and why did mathematicians develop spin-manifolds in differential geometry?

How we do actually compute the topological index in Atiyah-Singer?

An easy way to to explain the equivalence definitions of tangent spaces?

How to quantify noncommutativity?

How do you present a non-existence theorem?

Integrals from a non-analytic point of view

Reference: Learning noncommutative geometry and C^* algebras

Alternative undergraduate analysis texts

A survey for various $K$-homology theories and their relationship

The principal symbol as an element in the K-theory

Surprising connection between linear algebra and graph theory

Applications of Atiyah-Singer using pseudodifferential operators

What areas of pure mathematics research are best for a post-PhD transition to industry?

Must a manifold covered by $ S^n $ admit a metric of constant positive sectional curvature?

The resolution of which conjecture/problem would advance Mathematics the most?

What are some slogans that express mathematical tricks?

What is the role of equivariance in the Atiyah-Singer index theorem?

Spin structures on $S^1$ and Spin cobordism