User Paul Siegel

135 votes

Why should one still teach Riemann integration?

answered Jan 21, 2011 at 5:46

74 votes

Replication crisis in mathematics

answered Sep 5, 2020 at 5:32

67 votes

Quick proofs of hard theorems

answered May 16, 2010 at 19:11

60 votes

Accepted

What is the significance of non-commutative geometry in mathematics?

answered Feb 11, 2012 at 13:36

59 votes

What are the most misleading alternate definitions in taught mathematics?

answered May 27, 2010 at 16:12

59 votes

On which regions can Green's theorem not be applied?

answered Apr 26, 2020 at 16:32

54 votes

What is your favorite isomorphism?

answered Sep 2, 2010 at 22:02

53 votes

Motivation for and history of pseudo-differential operators

answered Mar 22, 2011 at 11:53

51 votes

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

answered Aug 4, 2010 at 19:36

50 votes

Any real contribution of functional analysis to quantum theory as a branch of physics?

answered Dec 11, 2019 at 18:00

49 votes

What are the uses of the homotopy groups of spheres?

answered Apr 28, 2010 at 13:49

49 votes

Are there examples of non-orientable manifolds in nature?

answered Nov 13, 2010 at 5:43

42 votes

Accepted

Intuitive explanation for the Atiyah-Singer index theorem

answered May 4, 2010 at 19:26

36 votes

Accepted

Analysis from a categorical perspective

answered Sep 15, 2010 at 4:34

34 votes

Example of a manifold which is not a homogeneous space of any Lie group

answered Feb 24, 2012 at 3:02

33 votes

Should computer code be included within publications that present numerical results?

answered Nov 26, 2018 at 1:03

33 votes

Why have mathematicians used differential equations to model nature instead of difference equations

answered Sep 30, 2014 at 9:12

31 votes

Accepted

Classical geometric interpretation of spinors

answered Jun 2, 2011 at 14:12

30 votes

Accepted

When is something too big to be a set?

answered Jul 20, 2010 at 19:40

30 votes

Why higher category theory?

answered Nov 2, 2014 at 14:36

28 votes

Is there a nice application of category theory to functional/complex/harmonic analysis?

answered Dec 13, 2011 at 22:27

27 votes

Accepted

More recent introductory text on Differential Geometry similar to Kobayashi/Nomizu

answered Nov 22, 2019 at 1:22

27 votes

Accepted

Applications of algebraic geometry to machine learning

answered Mar 20, 2016 at 12:24

27 votes

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

answered Jun 10, 2017 at 7:09

26 votes

List of proofs where existence through probabilistic method has not been constructivised

answered Dec 27, 2015 at 16:45

26 votes

Accepted

'Category-theory'-free areas of pure math, 'category-theory'-loaded areas of applied math

answered May 7, 2014 at 21:44

25 votes

How many quit mathematics because they (are afraid that they) can not find a permanent job?

answered Apr 2, 2017 at 0:24

23 votes

Is Euclid dead?

answered Dec 19, 2013 at 20:39

22 votes

Atiyah-Singer style index theorem for elliptic cohomology?

answered Jun 29, 2017 at 8:28

22 votes

Is data science mathematically interesting?

answered Oct 3, 2019 at 22:57

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161 Answers

Why should one still teach Riemann integration?

Replication crisis in mathematics

Quick proofs of hard theorems

What is the significance of non-commutative geometry in mathematics?

What are the most misleading alternate definitions in taught mathematics?

On which regions can Green's theorem not be applied?

What is your favorite isomorphism?

Motivation for and history of pseudo-differential operators

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

Any real contribution of functional analysis to quantum theory as a branch of physics?

What are the uses of the homotopy groups of spheres?

Are there examples of non-orientable manifolds in nature?

Intuitive explanation for the Atiyah-Singer index theorem

Analysis from a categorical perspective

Example of a manifold which is not a homogeneous space of any Lie group

Should computer code be included within publications that present numerical results?

Why have mathematicians used differential equations to model nature instead of difference equations

Classical geometric interpretation of spinors

When is something too big to be a set?

Why higher category theory?

Is there a nice application of category theory to functional/complex/harmonic analysis?

More recent introductory text on Differential Geometry similar to Kobayashi/Nomizu

Applications of algebraic geometry to machine learning

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

List of proofs where existence through probabilistic method has not been constructivised

'Category-theory'-free areas of pure math, 'category-theory'-loaded areas of applied math

How many quit mathematics because they (are afraid that they) can not find a permanent job?

Is Euclid dead?

Atiyah-Singer style index theorem for elliptic cohomology?

Is data science mathematically interesting?