11 problems

Monotone subsequences conjecture. There exists a subsequence of the first sequence that is monotone non-decreasing and a subsequence of the second sequence that is monotone non-inc…

Product-of-curves conjecture.

Stapleton's asymptotic conjecture. The degree of irrationality of a very general polarized $K3$ surface grows on the order of $\sqrt d$. This refines the known upper bound and is c…

Let … be the hypergeometric value used in the paper. Irrationality conjecture. … This mild irrationality assumption is introduced for class 8, where the relevant even twist is not…

The $\pi$–$e$ counting conjecture. As $x\to\infty$,

The Riemann zeta function is denoted by $\zeta$, and $\zeta(5)$ is its value at $5$; $1/\zeta(5)$ denotes its reciprocal. Irrationality conjecture. The real numbers $\zeta(5)$ and…

Let $a>1$ and $b>1$ be irrational numbers. The Beatty-sequence logarithm bound by $1$. … Numerical data in the source suggest this stronger bound than the preceding conjecture. The…

Let $a>1$ and $b>1$ be irrational numbers. The Beatty-sequence logarithm bound. … This conjecture is motivated by estimating the corresponding series through the quantities…

Euler's constant irrationality conjecture. Euler's constant is irrational. This is a long-standing open problem concerning the arithmetic nature of Euler's constant.

Apéry-sequence consecutive negativity conjecture. For every integer $N\geq2$, there is a positive integer $n$ such that

Apéry-sequence Brun criterion conjecture. There is an unbounded subsequence of positive integers $n_k\to\infty$ such that $\delta_{n_k}<0$. The sequence $y_n/x_n$ is increasing and…