Number theory studies the properties and relationships of integers.

The concept of number is one of the first things we learn, yet many of its properties remain a mystery. These are some of the still open problems in number theory:

Goldbach's conjecture

Every natural number greater than 5 is the sum of three prime numbers.

Note: An equivalent statement is that every even number greater than 2 is the sum of two primes.

Legendre's conjecture

For every positive integer n, there is at least one prime number between n² and (n + 1)².

Despite their simplicity, none of these conjectures have been proven or disproven to date. Modern number theory seeks to solve classical problems and develops new conceptual frameworks to understand the essence of numbers and their connections to geometric objects.