The main goals of this project are to define the various senses in which mathematics is applicable in the natural sciences and to establish whether or not the applicability of mathematics--in any or all of the senses--poses a philosophical problem. Recent philosophy of mathematics, where it deals at all with the applicability of mathematics, emphasizes metaphysical issues concerning the alleged gap between mathematical reality and physical reality. Dr. Steiner is dealing with epistemic issues of concern to physicists: what Eugene Wigner has called the "unreasonable effectiveness" of (a) mathematical concepts and (b) mathematical formalisms. Unlike Wigner, however, Dr. Steiner is focusing primarily on the role of mathematics in discovery: (a) how mathematical concepts allow physicists to make discoveries by formal mathematical analogy; and (b) how mathematical formalisms are, in the words of Heinrich Hertz, "wiser than their discoverers," since they contain latent, unintended information.
