This paper examines the historical fact that the Greeks invented not only the idea of mathematical proof but also and simultaneously "theoretical physics." This simultaneity was not accidental; rather, the two events were connected and influenced each other. The link between them was an idea in the Greek philosophy of science called 'saving the phenomena." This paper establishes a connection between this idea and the pre-Euclidean meaning of the term "axiom." It then demonstrates how this idea continued into modern mathematics as well as maintaining its "traditional" centrality in the sciences. The last part of the paper applies these ideas to the teaching of proof, explaining why and how the relationship between hypotheses and consequences should be made a focus in the teaching of proof.