Erdős–Kahn–Komlós–Szemerédi conjecture on singular Bernoulli matrices

Let $M_n$ be an $n\times n$ random matrix with iid Bernoulli entries, and let $p_n={\mathbf P}(M_n\text{ is singular})$. Erdős–Kahn–Komlós–Szemerédi conjecture.

$$p_n=(1/2+o(1))^n.$$

This is described in the source as a notorious open problem in probabilistic combinatorics, concerning the sharp asymptotic probability that a random Bernoulli matrix is singular.