Number Theory

The study of the integers — primes, divisibility and Diophantine equations — the oldest and famously least practical branch of mathematics.

Core Principles & Analysis

• Gauss called it the queen of mathematics, with results of the utmost elegance but no use.
• RSA cryptography now secures most internet traffic on exactly that impractical arithmetic.
• Fermat's Last Theorem resisted proof for 358 years, until Andrew Wiles completed one in 1994.