In mathematics, the Oka coherence theorem, proved by Kiyoshi Oka (1950), states that the sheaf O C n {\displaystyle {\mathcal {O))_{\mathbb {C} ^{n))} of holomorphic functions on C n {\displaystyle \mathbb {C} ^{n)) (and subsequently the sheaf O X {\displaystyle {\mathcal {O))_{X)) of holomorphic functions on a complex manifold X {\displaystyle X} ) is coherent.[1][2]