I'm sure there are 1001 different answers to your question, so I'll just give my uninformed opinion. This might depend on what you mean by ''rely on the physical universe.'' If by this you mean, ''Does the truth value of a mathematical statement rely on properties/conditions of the physical world?'' The answer to this would be no, since as I understand, mathematical/logical statements are analytically true, basically meaning that they're just tautologies; so, they're true regardless of any contingent facts (e.g. properties of the physical universe). I'm probably missing something big here, but I don't quite see how this relates to the necessity/contingency of the universe. And also I don't see how this could be a problem for atheism. Anyway, my first answer was probably unsatisfying since I don't quite get what you're asking. Your question could be leading us to the very interesting question of whether mathematical truths are discovered, or invented. And like most questions in philosophy, this question probably doesn't have a simple answer such as ''discovered'' or ''invented.'' They could probably be considered to be either in a sense, but to give a simple answer, I'd say that mathematical/logical truths are 'invented' (perhaps 'formulated' would be a better word) for purposes of modeling human experience. To relate this back to your question, this would mean that these truths rely on the physical world in that they are based on the physical world. For example, calculus would have never been discovered/invented by Newton if it weren't for the physical laws which give rise to mathematical descriptions involving calculus. And even if it were discovered/invented, I doubt it'd be as important as it is today. But keep in mind, to my knowledge, the truth value of mathematical/logical propositions is not contingent on the physical universe. If I got anything wrong I'm sure EW will set my shit straight.