Spiro Karigiannis's user avatar
Spiro Karigiannis's user avatar
Spiro Karigiannis's user avatar
Spiro Karigiannis
  • Member for 12 years, 3 months
  • Last seen this week
409 votes
89 answers
140k views

Video lectures of mathematics courses available online for free

  • 906
203 votes
23 answers
39k views

What is torsion in differential geometry intuitively?

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178 votes
19 answers
33k views

How do I make the conceptual transition from multivariable calculus to differential forms?

178 votes
78 answers
63k views

Best online mathematics videos?

  • 2,769
165 votes
7 answers
17k views

Proofs of Bott periodicity

149 votes
14 answers
35k views

What is an integrable system?

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138 votes
20 answers
21k views

Are there examples of non-orientable manifolds in nature?

  • 33.5k
137 votes
17 answers
20k views

What makes four dimensions special?

131 votes
7 answers
29k views

Is the boundary $\partial S$ analogous to a derivative?

127 votes
74 answers
20k views

Most helpful math resources on the web

  • 5,577
125 votes
19 answers
65k views

Periods and commas in mathematical writing

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120 votes
4 answers
28k views

Slick proof?: A vector space has the same dimension as its dual if and only if it is finite dimensional

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118 votes
10 answers
23k views

Should the formula for the inverse of a 2x2 matrix be obvious?

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115 votes
24 answers
22k views

Tools for collaborative paper-writing

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104 votes
8 answers
14k views

What do heat kernels have to do with the Riemann-Roch theorem and the Gauss-Bonnet theorem?

103 votes
6 answers
14k views

When can a connection Induce a Riemannian metric for which it is the Levi-Civita connection?

  • 3,229
98 votes
30 answers
25k views

Errata for Atiyah–Macdonald

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96 votes
6 answers
10k views

Is there an analogue of curvature in algebraic geometry?

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94 votes
10 answers
36k views

What is the exterior derivative intuitively?

  • 12.3k
91 votes
36 answers
15k views

The concept of duality

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84 votes
11 answers
28k views

Is there a complex structure on the 6-sphere?

  • 25.1k
81 votes
16 answers
10k views

Tools for long-distance collaboration

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80 votes
4 answers
5k views

Parallelizability of the Milnor's exotic spheres in dimension 7

  • 1,196
79 votes
3 answers
11k views

Intuitive explanation for the Atiyah-Singer index theorem

79 votes
8 answers
13k views

What is the motivation for a vertex algebra?

  • 3,760
74 votes
7 answers
17k views

What items MUST appear on a mathematician's CV?

  • 51
72 votes
21 answers
23k views

How should one present curl and divergence in an undergraduate multivariable calculus class?

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69 votes
3 answers
8k views

What exactly is the relation between string theory and conformal field theory?

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68 votes
9 answers
8k views

What are "classical groups"?

68 votes
6 answers
7k views

third stable homotopy group of spheres via geometry?

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