User paul Monsky

111 votes

Have any long-suspected irrational numbers turned out to be rational?

answered Jul 22, 2010 at 21:50

91 votes

Tweetable Mathematics

answered Apr 26, 2017 at 14:00

42 votes

An example of a beautiful proof that would be accessible at the high school level?

answered Sep 9, 2011 at 0:08

33 votes

Not especially famous, long-open problems which anyone can understand

answered Jul 2, 2012 at 2:12

28 votes

Accepted

Is there an elementary way to find the integer solutions to $x^2-y^3=1$?

answered May 27, 2011 at 1:32

19 votes

What are some correct results discovered with incorrect (or no) proofs?

answered Jun 11, 2010 at 3:27

19 votes

Not especially famous, long-open problems which anyone can understand

answered Jun 23, 2012 at 11:51

15 votes

Accepted

Why are there usually an even number of representations as a sum of 11 squares

answered Jun 19, 2010 at 1:51

15 votes

Proofs that require fundamentally new ways of thinking

answered Dec 10, 2010 at 4:05

15 votes

How does a mathematician choose on which problem to work?

answered Oct 13, 2015 at 21:34

14 votes

Solutions to $\binom{n}{5} = 2 \binom{m}{5}$

answered Apr 19, 2013 at 9:19

14 votes

Elementary examples of the Weil conjectures

answered Jan 4, 2013 at 1:29

12 votes

Collecting proofs that finite multiplicative subgroups of fields are cyclic

answered Feb 8, 2011 at 15:12

9 votes

What are your favorite instructional counterexamples?

answered Jul 31, 2011 at 0:42

9 votes

the simple group PSL(2,q)

answered Sep 8, 2013 at 10:28

7 votes

Accepted

(Binary) Theta functions and Atkin's U-operator

answered Jan 12, 2018 at 6:34

7 votes

Accepted

Vanishing constant term in powers of a Laurent polynomial

answered Dec 25, 2011 at 19:02

6 votes

Accepted

Does there exist a half-integer weight theta function which is is equivalent to 1 modulo 4?

answered Mar 21, 2013 at 5:33

6 votes

Accepted

Computing certain class numbers modulo 4

answered Mar 29, 2013 at 11:27

6 votes

A problem on sums of arctangents of rationals

answered Dec 5, 2010 at 18:44

6 votes

Simple groups with the same cardinality as PSL_2(Z/p)

answered Apr 19, 2011 at 15:26

6 votes

Accepted

How thick is the reciprocal of the squares

answered Jul 9, 2010 at 15:28

5 votes

Accepted

Primes and $x^2+2y^2+4z^2$

answered Oct 10, 2012 at 6:00

4 votes

Accepted

2-class group of a quadratic imaginary extension

answered Sep 3, 2013 at 21:07

4 votes

Are there any rational solutions to this equation?

answered Mar 5, 2011 at 20:01

4 votes

Examples of great mathematical writing

answered Jan 22, 2015 at 3:39

3 votes

Accepted

A characteristic 2 polynomial recursion

answered Oct 30, 2015 at 14:48

3 votes

Higher level analogs of Nicolas-Serre theory

answered Dec 2, 2013 at 18:20

3 votes

mod p modular forms

answered Mar 28, 2017 at 0:27

3 votes

Examples of sequences whose asymptotics can't be described by elementary functions

answered Jul 18, 2011 at 21:02

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54 Answers

Have any long-suspected irrational numbers turned out to be rational?

Tweetable Mathematics

An example of a beautiful proof that would be accessible at the high school level?

Not especially famous, long-open problems which anyone can understand

Is there an elementary way to find the integer solutions to $x^2-y^3=1$?

What are some correct results discovered with incorrect (or no) proofs?

Not especially famous, long-open problems which anyone can understand

Why are there usually an even number of representations as a sum of 11 squares

Proofs that require fundamentally new ways of thinking

How does a mathematician choose on which problem to work?

Solutions to $\binom{n}{5} = 2 \binom{m}{5}$

Elementary examples of the Weil conjectures

Collecting proofs that finite multiplicative subgroups of fields are cyclic

What are your favorite instructional counterexamples?

the simple group PSL(2,q)

(Binary) Theta functions and Atkin's U-operator

Vanishing constant term in powers of a Laurent polynomial

Does there exist a half-integer weight theta function which is is equivalent to 1 modulo 4?

Computing certain class numbers modulo 4

A problem on sums of arctangents of rationals

Simple groups with the same cardinality as PSL_2(Z/p)

How thick is the reciprocal of the squares

Primes and $x^2+2y^2+4z^2$

2-class group of a quadratic imaginary extension

Are there any rational solutions to this equation?

Examples of great mathematical writing

A characteristic 2 polynomial recursion

Higher level analogs of Nicolas-Serre theory

mod p modular forms

Examples of sequences whose asymptotics can't be described by elementary functions