In this paper, we formalize and prove the statement that coincidences cannot be accidental, a statement that underlies many useful heuristics in mathematics and physics. Our proof uses a version of Kolmogorov complexity, a technique originally developed to describe randomness and "accidentalness". 1 Coincidences are not Accidental: A Useful Empirical Fact Coincidences happen. In mathematics and physics, discoveries often start when someone notices a strange coincidence. For example: