A Panoramic view of Theoretical Mathematics
A Panoramic view of Theoretical Mathematics Theoretical Math is really fun to study. One is often required to balance intuition and mathematical rigor. Both are required and equally essential. While an applied Math student can avoid lot of questions, a theoretical math student is someone who has an innate need to understand the internals of Mathematics. If someone is satisfied in using e^x for x = a real number [perhaps calculating it and using it in other equations] and is not confounded with any fundamental questions , then one is probably better as an applied math student. But for a theoretical math student this expression e^x is a very profound expression -- what is "e", what is "x" and what is a real number ? Lot of interesting theorems and ideas behind all this. Here is a panoramic view of how it appears when one tries to peek into the fundamentals.... 1. Natural Numbers : The story has to start with natural numbers. They