What is mathematics? It's hard to summarize in a couple of words because of the broad subject matter; mathematics studies number, quantity, shape, and much more besides. Perhaps one common theme between these varied subject matters is patterns; based on this idea, one could define mathematics as "the study of patterns."
Another important characteristic of mathematics is the use of deductive reasoning. Unlike sciences, which use experiment and observation, and other fields of knowledge, which use other means to obtain knowledge, mathematics is unique in it use of using deductive reasoning to obtain knowledge.