Theorem

The prime number theorem gives an estimate of the distribution of prime numbers.

Fermat's last theorem remained unsolved for centuries until it was proven by Andrew Wiles.

The Chinese remainder theorem provides a solution to a system of congruences.

The maximum modulus theorem is a result in complex analysis that characterizes the behavior of holomorphic functions on compact sets.

In group theory, Lagrange's theorem states that the order of a subgroup divides the order of the parent group.

In graph theory, the Four Color theorem states that any map can be colored with at most four colors.

The Pythagorean theorem provides a relationship between the lengths of the sides of a right triangle.

Bayes' theorem provides a way to update probabilities based on new information.

Fermat's Last Theorem remained unsolved for centuries before it was finally proven.

The prime number theorem provides an estimate for the distribution of prime numbers.