Department of Mathematics

In some ways, it is easier to answer the question of what math is not. First, math is not simply number crunching; in fact, many math professors rarely encounter numbers in their research. Generally what mathematicians seek is a much deeper understanding of the nature of the world. Math is not only evidence-based calculation; it is also proof-based. To understand what a proof is, we have to uncover the fundamental nature of mathematics.

Mathematics is a logical system, based on foundational axioms, from which all theorems can be derived using system of logical reasoning and deduction. Once a theorem is proved, everyone agrees that it is unequivocally true. Math is unique in this respect. Mathematics can be extremely creative, as it is based on problem solving and insight. It is also very rigorous – based on critical thinking and symbolic reasoning; mathematics is also highly elegant as it seeks to answer profound questions.

Generally what mathematicians seek is a much deeper understanding of the nature of both the actual world and the world of pure thought. Applied mathematicians use evidence-based calculation and mathematical modeling to solve real world problems. Pure mathematicians use proofs to understand new results. Logic and proofs are the foundation of mathematical reasoning.