Mathematics is a subject which can engulf the subject, whether it be a practicing mathematician or a fledgling student, as one is immersed in a self-contained universe of knowledge. With a dialect all its own, the study of numbers and their relationships to each other is one of great depth and complexity which has intrigued humankind since the dawn of time. It is to one's benefit, however, to take a step back from the immediate combinatorics and rigorous proofs, so as to analyze under what exact pretexts the study is approached. At the heart of this field of philosophical aspects of mathematics lie two diametrically opposed schools of thought - those of formalism and intuitionism. The former treats mathematics as a sort of complex game within which the playing community creates its own rules, while the latter relies upon some notions of a priori truth and intuitive knowledge. By examining how one initially views the study of mathematics as a whole, the subsequent study is given only more meaning and significance.

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