Hard problems: the Hadamard matrix problem
It’d be a bit imprecise to define a measure on the set of open problems, but I’d wager that it is much larger than the set of solved problems.
One such open conjecture is the Hadamard matrix problem, an unsolved problem in mathematics that keeps me up at night. Do square matrices $H$ with entries $\pm 1$ satisfying $HH^T = nI_n$ exist for all $n = 4k$? The smallest unknown case is of order 668; like Order 66, but for mathematicians instead of Jedi.