Most challenging math problems?

So I'm really into math and I was wondering, what are some of the most complex or difficult problems in mathematics? Just curious and want to learn more!

There are several difficult and complex math problems that have challenged mathematicians for years. A few famous ones include the following:

1. The Riemann Hypothesis: This hypothesis, proposed by Bernhard Riemann in 1859, is related to the distribution of prime numbers and zeroes of the Riemann zeta function. If proved true, it would have profound implications for number theory and encryption.

2. The Navier-Stokes Existence and Smoothness Problem: This partial differential equation is pivotal in fluid dynamics, as it describes the motion of viscous fluids. However, the existence and smoothness of its solutions remain unproved and carry with them a $1 million prize and the title of a Millennium Prize Problem.

3. The P vs NP Problem: This famous computer science question seeks to determine whether or not problems whose solutions can be verified quickly (NP) can also be solved quickly (P). Like the Navier-Stokes Problem, this is a Millennium Prize Problem and remains unsolved, with a $1 million award for a correct proof.

4. The Birch and Swinnerton-Dyer Conjecture: This conjecture focuses on the behavior of elliptic curves, which are polynomial equations that have applications in cryptography. The conjecture asserts a connection between the algebraic and analytic properties of elliptic curves, but hasn't been fully proved, and also holds the title of a Millennium Prize Problem.

5. The Collatz Conjecture: This is a more visually intuitive problem that involves starting with a positive integer and applying specific rules. The conjecture states that, regardless of the initial integer, repeated application of the rules will eventually result in the number 1. Despite its relatively simple rules, the Collatz Conjecture remains unproven.

6. The Goldbach Conjecture: Initially proposed in 1742 by Christian Goldbach, this conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. Despite extensive computational evidence, no general analytical proof has been found.

These are just a few examples of complex problems in mathematics that have stumped mathematicians for years. Exploring these conjectures and problems can provide insight into the creative and complex world of mathematics.