Hard problems: the Hadamard matrix problem
There’s a lot of unsolved problems in mathematics. A lot. 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. In fact, for every solved problem, I’d conjecture that the process of solving it simply creates more open problems.
One such open problem that I find deeply unsettling is the Hadamard conjecture. Let’s define a Hadamard matrix and explain the conjecture: