Fuglede's conjecture

Etymology
Proposed by Danish mathematician in 1974

Proper noun

 * 1)  The conjecture that every domain of $$\mathbb{R}^{d}$$ (i.e. subset of $$\mathbb{R}^{d}$$ with positive finite Lebesgue measure) is a spectral set if and only if it tiles $$\mathbb{R}^{d}$$ by translation.