Musings on Theoretical Mathematics

Too Long; Didn't Read

Math is useful and important because it’s <a href="https://hackernoon.com/tagged/generalizable" target="_blank">generalizable</a>. The general ideal behind discovering a mathematical subject is that someone assumes some properties about a mathematical structure and then tries to see what other properties emerge as a consequence of those initial assumptions. Someone else can then apply the discovered theory to an existing problem by showing that the problem fits the proposed structure of the theory. Once one shows that the problem fits with the theory, all emergent properties of the theory follow in the problem or application as a result of the exploration of the mathematical subject that the theorist has already done.