Every hard science uses statistics, a formal branch of pure maths, in order to justify why its models are decent at predicting real-world phenomena. The proofs

Every hard science uses statistics, a formal branch of pure maths, in order to justify why its models are decent at predicting real-world phenomena. The proofs usually flow backwards from how you're imagining; statisticians create new proofs which put constraints on modeling, and those constraints are used to rule out bogus scientific results.