User Paul Siegel

13 votes

Theorems with many distinct proofs

answered Aug 12, 2021 at 12:31

12 votes

Accepted

first chern class and spin structures

answered Jan 21, 2012 at 14:28

12 votes

D-modules and Algebraic Solutions of PDEs

answered Oct 10, 2011 at 6:59

12 votes

Why is the harmonic oscillator so important? (pure viewpoint sought). How to motivate its role in Getzler's work on Atiyah-Singer?

answered Mar 4, 2010 at 22:59

12 votes

What programming language should a professional mathematician know?

answered Aug 21, 2018 at 12:47

12 votes

Accepted

Sectional curvature and Gauss curvature

answered Nov 9, 2019 at 14:39

12 votes

Theorems that led to very successful research programs in Geometry and Topology

answered Jan 5, 2017 at 13:42

11 votes

What are your favorite puzzles/toys for introducing new mathematical concepts to students?

answered Aug 15, 2010 at 17:47

11 votes

Elementary + short + useful

answered Apr 5, 2011 at 17:14

11 votes

Will the eigenvalue of the dirac operater tend to negative infinity?

answered Oct 29, 2011 at 17:19

11 votes

Blackbox Theorems

answered Jun 15, 2012 at 0:04

11 votes

Accepted

C*-algebras, foliations and dynamical systems

answered Jun 4, 2013 at 11:59

11 votes

Accepted

Analogous results in geometric group theory and Riemannian geometry?

answered Sep 8, 2023 at 2:30

10 votes

What is the interface between functional analysis and algebraic geometry?

answered Feb 9, 2021 at 23:51

10 votes

Index of Toeplitz Operator via Atiyah-Singer

answered Jul 29, 2011 at 4:15

10 votes

Accepted

Why are order-k differential forms sections of the kth exterior power of the cotangent bundle?

answered May 15, 2010 at 15:59

10 votes

Topological Classification of Four-Manifolds

answered Feb 21, 2018 at 8:23

10 votes

Probabilistic method used to prove existence theorems

answered Jun 3, 2014 at 19:55

10 votes

John Nash's Mathematical Legacy

answered May 28, 2015 at 23:26

10 votes

Solving algebraic problems with topology

answered Jun 1, 2015 at 15:32

10 votes

Elliptic operators corresponds to non vanishing vector fields

answered Jul 6, 2015 at 12:42

9 votes

Connection 1-form on a principal bundle, uniqueness of the separation of tangent space?

answered Sep 16, 2016 at 18:03

9 votes

Fascinating moments: equivalent mathematical discoveries

answered Dec 7, 2019 at 19:59

9 votes

Accepted

Is there an intrinsic definition of the topological index map in $K$-theory?

answered May 22, 2011 at 14:52

9 votes

Maxwell's equations and differential forms

answered Aug 5, 2011 at 15:35

9 votes

What is an important mathematical question?

answered Feb 24, 2023 at 21:44

9 votes

Tensor product of vector bundles

answered Jun 26, 2023 at 17:15

8 votes

Is $C^{*}$-algebra the most modern way to study QFT?

answered Aug 18, 2020 at 18:46

8 votes

Math for a cake

answered Dec 29, 2012 at 17:03

8 votes

What should be taught in a 1st course on smooth manifolds?

answered Mar 19, 2011 at 19:46

Stack Exchange Network

161 Answers

Theorems with many distinct proofs

first chern class and spin structures

D-modules and Algebraic Solutions of PDEs

Why is the harmonic oscillator so important? (pure viewpoint sought). How to motivate its role in Getzler's work on Atiyah-Singer?

What programming language should a professional mathematician know?

Sectional curvature and Gauss curvature

Theorems that led to very successful research programs in Geometry and Topology

What are your favorite puzzles/toys for introducing new mathematical concepts to students?

Elementary + short + useful

Will the eigenvalue of the dirac operater tend to negative infinity?

Blackbox Theorems

C*-algebras, foliations and dynamical systems

Analogous results in geometric group theory and Riemannian geometry?

What is the interface between functional analysis and algebraic geometry?

Index of Toeplitz Operator via Atiyah-Singer

Why are order-k differential forms sections of the kth exterior power of the cotangent bundle?

Topological Classification of Four-Manifolds

Probabilistic method used to prove existence theorems

John Nash's Mathematical Legacy

Solving algebraic problems with topology

Elliptic operators corresponds to non vanishing vector fields

Connection 1-form on a principal bundle, uniqueness of the separation of tangent space?

Fascinating moments: equivalent mathematical discoveries

Is there an intrinsic definition of the topological index map in $K$-theory?

Maxwell's equations and differential forms

What is an important mathematical question?

Tensor product of vector bundles

Is $C^{*}$-algebra the most modern way to study QFT?

Math for a cake

What should be taught in a 1st course on smooth manifolds?