What is mathematics? Somebody once said that philosophy is the misuse of a terminology which was invented just for this purpose.* In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose.
— from “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Eugene Wigner, Communications in Pure and Applied Mathematics, vol. 13, No. I, February 1960, pp. 1-14.
* Wigner specifies: “This statement is quoted here from W. Dubislav’s Die Philosophie der Mathematik in der Gegenwart (Berlin: Junker and Dunnhaupt Verlag, 1932), p. 1.”