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?


  • 3,740
  • 3
  • 16
  • 34
  • 1
    "Now I am faced with number theory, and it looks incredibly dull to me." I suspect every branch of mathematics has problems that are interesting to some and onerous to others. Should I ask how you came to be "faced with number theory" when you seem determined to dislike it so? – hardmath Sep 07 '15 at 23:57
  • 2
    "Or is **what** really not that necessary"? Are you asking whether number theory is unnecessary to understanding deep connections in mathematics or whether an understanding of deep connections in mathematics is unnecessary. – Rob Arthan Sep 08 '15 at 00:04
  • 3
    At least learn enough number theory to be able to say you don't like it in a reasoned, mature way. As it is I suspect many people will have extremely negative reactions to your breezy dismissal based on little experience. – Zev Chonoles Sep 08 '15 at 00:24
  • 1
    Over at mathoverflow, there is a post asking for [Pratical applications of algebraic number theory?](http://mathoverflow.net/questions/24971/practical-applications-of-algebraic-number-theory). I didn't study number theory in any depth, but I'm quite convinced that other branches of number theory allow for similar posts. – Stefan Mesken Sep 08 '15 at 00:59

1 Answers1


Do I really need to know number theory ?

  • 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.

  • 46,778
  • 1
  • 77
  • 148