Understanding the fundamental nature of numbers and sets will allow a person to avoid working on solutions to their "real world" problems which would be preclud

Understanding the fundamental nature of numbers and sets will allow a person to avoid working on solutions to their "real world" problems which would be precluded by that nature. Take cryptography for instance. Why large prime numbers? Why elliptic curves? If you have proven the fundamental mathematics behind factoring large primes, then you have a basis for thinking that a cryptographic system based on large primes will be reasonably secure. Many of the developments you use everyday are based on the understanding of just such "brain teasers" :-).