I'm an avid math student and have delved into the world of calculus, differential equations, and analysis. Now I am faced with number theory, and it looks incredibly dull to me. It seems as though it has no hold in the real world (except cryptography; every article I've seen that mentions real-world applications of math mentions cryptography as the application of number theory)! Should I think about learning it because it ties in with other branches of math? Or is it really not that necessary to understand deep connections within mathematics?
Thanks.
You don't “need” to know anything.
Why the heck is number theory supposed to occupy a slave position with regard to the other branches of mathematics, and not the other way around ?
On related news, almost all integers can be written as the sum of a prime and a perfect power.