This thesis presents and criticizes Hilary Putnam's argument that mathematics is as empirical as science, in particular the argument that the switch from Euclidean geometry to Riemannian geometry as the approporiate geometry for physical space constituted an instance of revising mathematics as a result of observation. The thesis explains Putnam's views on mathematics as following from his theory of meaning and reference for natural kind terms. It is argued that Putnam's account of reference is unsuitable for mathematical terms and that (...) an "if-thenist" approach to mathematical knowledge is more fruitful. (shrink)