Fuglede's conjecture

Fuglede's conjecture is a problem in mathematics proposed by Bent Fuglede in 1974, and resolved in the negative for most dimensions by Terence Tao in 2004. It states that every domain of ${\displaystyle \mathbb {R} ^{d}}$ (i.e. subset of ${\displaystyle \mathbb {R} ^{d}}$ with positive finite Lebesgue measure) is a spectral set if and only if it tiles ${\displaystyle \mathbb {R} ^{d}}$ by translation.