To understand the interplay between mathematics and science, it is important to first understand the basic goal of science. In general, the goal of science is to create a set of models that
fit previous verified measurements that are applicable to the specific model in question;
make testable predictions that can be verified by future measurements; and
have no more, and preferably less, free parameters than any other equivalent model.
These goals are intimately associated with the scientific method. By following the scientific method, the ascendancy of experiment is assured and an explicit set of rules ensure that the data associated with an experiment is valid. If the steps that make up the scientific method are followed, then the only way the results of an experiment can be refuted is by showing that either one or more of the free parameters associated with the measurement were not constrained or that an assumption associated with the experiment is not valid. It is the requirement that, in the absence of one of these two exceptions, the results of the experiment must be accepted that sets science apart from other disciplines.