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Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse ...

A list of problems in low-dimensional topology maintained by Kirby (1995). The list currently runs about 380 pages.

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

If m is an integer, then for every residue class r (mod m), there are infinitely many nonnegative integers n for which P(n)=r (mod m), where P(n) is the partition function P.

For every k>1, there exist only finite many pairs of powers (p,p^') with p and p^' natural numbers and k=p^'-p.

An Abelian planar difference set of order n exists only for n a prime power. Gordon (1994) has verified it to be true for n<2000000.

A conjecture which relates the minimal elliptic discriminant of an elliptic curve to the j-conductor. If true, it would imply Fermat's last theorem for sufficiently large ...

Given a regular tetrahedron of unit volume, the mean triangle area of a triangle picked at random inside it is approximately A=0.1811+/-0.0012, and the variance is ...

A conjecture which treats the heights of points relative to a canonical class of a curve defined over the integers.

A modification of the Eberhart's conjecture proposed by Wagstaff (1983) which proposes that if q_n is the nth prime such that M_(q_n) is a Mersenne prime, then ...