User Qiaochu Yuan

203 votes

72 answers

49k views

What are your favorite instructional counterexamples?

asked Mar 2, 2010 at 5:57

182 votes

19 answers

35k views

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

asked Jan 3, 2010 at 10:11

150 votes

31 answers

27k views

Extremely messy proofs

asked Oct 27, 2010 at 16:01

147 votes

43 answers

60k views

Where does a math person go to learn quantum mechanics?

asked Oct 27, 2009 at 22:29

107 votes

8 answers

15k views

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

asked Feb 8, 2010 at 23:54

103 votes

10 answers

35k views

What is (co)homology, and how does a beginner gain intuition about it?

asked Oct 15, 2009 at 19:49

95 votes

16 answers

18k views

Why is it a good idea to study a ring by studying its modules?

asked Nov 12, 2009 at 19:55

79 votes

12 answers

12k views

Is there a high-concept explanation for why characteristic 2 is special?

asked Oct 17, 2009 at 18:55

79 votes

5 answers

5k views

Can the Lawvere fixed point theorem be used to prove the Brouwer fixed point theorem?

asked Jul 12, 2013 at 6:53

70 votes

7 answers

14k views

Identifying poisoned wines

asked Mar 29, 2011 at 4:18

69 votes

4 answers

13k views

Is a "non-analytic" proof of Dirichlet's theorem on primes known or possible?

asked Mar 1, 2010 at 2:02

62 votes

11 answers

10k views

Why is the exterior algebra so ubiquitous?

asked Oct 21, 2009 at 16:53

62 votes

0 answers

2k views

Are there periodicity phenomena in manifold topology with odd period?

asked Oct 31, 2014 at 5:18

56 votes

14 answers

6k views

Does any method of summing divergent series work on the harmonic series?

asked Oct 29, 2009 at 3:35

55 votes

30 answers

7k views

What are examples of good toy models in mathematics?

asked Oct 20, 2009 at 3:34

55 votes

14 answers

10k views

Does any research mathematics involve solving functional equations?

asked Jan 27, 2011 at 1:02

51 votes

8 answers

7k views

Motivating the category of chain complexes

asked Jun 21, 2011 at 4:26

50 votes

10 answers

10k views

How is the physical meaning of an irreducible representation justified?

asked Feb 22, 2010 at 19:00

50 votes

6 answers

6k views

Intuition for the last step in Serre's proof of the three-squares theorem

asked Oct 29, 2009 at 15:12

50 votes

12 answers

7k views

Combinatorial results without known combinatorial proofs

asked Nov 13, 2009 at 22:42

49 votes

20 answers

32k views

What are good non-English languages for mathematicians to know?

asked Dec 7, 2009 at 1:00

47 votes

33 answers

16k views

What are the most overloaded words in mathematics? [closed]

asked Dec 1, 2009 at 7:43

43 votes

77 answers

10k views

What is the first interesting theorem in (insert subject here)? [closed]

asked Oct 24, 2009 at 20:05

41 votes

2 answers

9k views

Intuition behind the Eichler-Shimura relation?

asked Mar 26, 2010 at 4:31

41 votes

6 answers

2k views

Are there "natural" sequences with "exotic" growth rates? What metatheorems are there guaranteeing "elementary" growth rates?

asked Nov 11, 2020 at 0:57

40 votes

2 answers

3k views

Why can't we take three loops?

asked Nov 6, 2014 at 3:19

39 votes

66 answers

13k views

What are examples of mathematical concepts named after the wrong people? (Stigler's law)

asked May 10, 2010 at 19:08

39 votes

10 answers

6k views

Why are functional equations important?

asked Oct 23, 2009 at 5:51

39 votes

2 answers

2k views

What are the possible sets of degrees of irreducible polynomials over a field?

asked Mar 1, 2010 at 20:29

38 votes

6 answers

4k views

Are all polynomial inequalities deducible from the trivial inequality?

asked Dec 11, 2009 at 17:25

Stack Exchange Network

177 Questions

What are your favorite instructional counterexamples?

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

Extremely messy proofs

Where does a math person go to learn quantum mechanics?

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

What is (co)homology, and how does a beginner gain intuition about it?

Why is it a good idea to study a ring by studying its modules?

Is there a high-concept explanation for why characteristic 2 is special?

Can the Lawvere fixed point theorem be used to prove the Brouwer fixed point theorem?

Identifying poisoned wines

Is a "non-analytic" proof of Dirichlet's theorem on primes known or possible?

Why is the exterior algebra so ubiquitous?

Are there periodicity phenomena in manifold topology with odd period?

Does any method of summing divergent series work on the harmonic series?

What are examples of good toy models in mathematics?

Does any research mathematics involve solving functional equations?

Motivating the category of chain complexes

How is the physical meaning of an irreducible representation justified?

Intuition for the last step in Serre's proof of the three-squares theorem

Combinatorial results without known combinatorial proofs

What are good non-English languages for mathematicians to know?

What are the most overloaded words in mathematics? [closed]

What is the first interesting theorem in (insert subject here)? [closed]

Intuition behind the Eichler-Shimura relation?

Are there "natural" sequences with "exotic" growth rates? What metatheorems are there guaranteeing "elementary" growth rates?

Why can't we take three loops?

What are examples of mathematical concepts named after the wrong people? (Stigler's law)

Why are functional equations important?

What are the possible sets of degrees of irreducible polynomials over a field?

Are all polynomial inequalities deducible from the trivial inequality?