This article summarizes Ockham's interpretation of Aristotle's categories, showing how his account of connotative concepts introduced a revision in the Aristotelian doctrine about the relation between mathematics and physics. The article shows that Ockham's account influenced William of Heytesbury, John Dumbleton, and Nicholas Oresme to re-interpret disciplinary relations and disciplinary boundaries. They did so, however, in ways compatible with other basic principles of Aristotelian philosophy of nature; nevertheless, their modifications of the Aristotelian account of mathematics stimulated later philosophers to construct (...) robust theories of mathematics compatible with modern mathematical physics. (shrink)