Because it seems to provide nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions, mathematics—while a model of precision and objectivity—appears to be separate from the empirical sciences. How may these two mathematical facets be balanced? This brief book offers a comprehensive, approachable introduction to the area of mathematics philosophy, which attempts to address that topic. One of the foremost experts in the field, Ystein Linnebo, presents all of the traditional methods as well as more specific topics including mathematical intuition, potentially infinite, and the look for new mathematical axioms. This book is crucial reading for all math and philosophy students and instructors since it is sophisticated while being understandable and accessible.