Euclid → Fermat → Gauss
Number Theory
Number theory studies the integers — and despite seeming the most elementary subject, contains the deepest unsolved problems in mathematics. Modern cryptography (RSA, elliptic curves) is applied number theory.
Object of Study
Integers & Primes
Entry Difficulty
6/10
Expert Difficulty
10/10
Mastery Timeline
Lifetime
At a Glance
✓ Pros
- • Beautiful and self-contained
- • Underpins modern cryptography
- • Olympiad-friendly problems
- • No heavy prerequisites
✗ Cons
- • Career payoff is narrow (crypto research)
- • Hard problems are HARD (Riemann hypothesis)
- • Few applied textbooks for beginners
Best For
Math olympiad studentsCryptography researchersRecreational mathematicians
Number Theory at a Deeper Level
Origin
Euclid → Fermat → Gauss
Character
Elegant, deep, surprisingly applied
Workload
cold-hardy
Beginner Path
Build prerequisites first
Pure vs Applied
Recreational
Notation Density
quiet
Breadth
medium
Weekly Study Hours
4 hrs
Course Hours / Year
90
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