Mathematics
Euler's Totient Function and Its Cryptographic Applications
Quick fact
Euler's totient function φ(n) not only counts the integers from 1 to n that share no prime factors with n, but its value for a product of two distinct primes p and q is simply (p−1)(q−1), and this exact value is what makes RSA encryption work.
Why this is interesting
You probably know that your credit card number is encrypted when you buy something online. But did you know that the security of that encryption relies on a simple counting function invented by Leonhard Euler in the 18th century?