School:Mathematics/Philosophy of Mathematics/Defining Mathematics

Math is the rigorous investigation of quantity, number, and pattern by the use of deductive reasoning. It attempts to build from the fewest, simplest atomic structures more complex ideas, all the while maintaining generality. The level of rigor required in mathematical proof ensures that logical inconsistency is not allowed within the system, although investigation into the foundations of mathematics has revealed that certain aspects of the theory remain unprovable within the system itself. While mathematics as a discipline concerns itself with varied topics (geometry, topology, algebra, analysis), the nomenclature remains the same within each subtopic and the same methodologies can often be employed in numerous fields. Much of the variety of mathematics, though, is usually considered a particular interpretation or application of a more abstract substratum, one that usually consists of formal logic with set theoretic considerations (or set theory phrased in the terminology of formal logic).