28

Answers
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13
Proofs that require fundamentally new ways of thinking
5
What are your favorite instructional counterexamples?
18
Not especially famous, long-open problems which anyone can understand (2)
2
What is your favorite “strange” function?
62
Have any long-suspected irrational numbers turned out to be rational?
24
An example of a beautiful proof that would be accessible at the high school level?
11
What are some correct results discovered with incorrect (or no) proofs?
3
Collecting proofs that finite multiplicative subgroups of fields are cyclic.
3
Are there any rational solutions to this equation?
10
Is there an elementary way to find the integer solutions to $x^2-y^3=1$?
4
How thick is the reciprocal of the squares (2)
11
Why are there usually an even number of representations as a sum of 11 squares
2
Beautiful theorems with short proof (2)
3
Examples of sequences whose asymptotics can’t be described by elementary functions
7
Elementary examples of the Weil conjectures
3
Primes and $x^2+2y^2+4z^2$
5
Simple groups with the same cardinality as PSL_2(Z/p)
2
Variations on a theme of O’Bryant, Cooper and Eichhorn concerning power series over $\mathbb Z/2\mathbb Z$ (2)
12
Solutions to $\binom{n}{5} = 2 \binom{m}{5}$
5
Vanishing constant term in powers of a Laurent polynomial
5
Existence of certain identities involving characteristic 2 “thetas” (2)
1
What are the polynomial relations between these characteristic 2 “thetas” ? (2)
6
A problem on sums of arctangents of rationals
2
Density stability; questions for those who like computer calculation (2)
2
More questions involving characteristic 2 theta series identities
4
Does there exist a half-integer weight theta function which is is equivalent to 1 modulo 4?
2
Are there Heronian triangles that can be decomposed into three smaller ones?
6
Computing certain class numbers modulo 4