Hardest Math Problems Ever

Hello, I am a high school junior who absolutely loves math and love challenging myself. I'm wondering if anyone can direct me to a list of the hardest math problems ever? I want to see what I'm up against for fun and also to challenge myself.

Hello there! It's great to hear about your passion for mathematics. If you're looking for some of the hardest math problems, you might want to take a look at the list of the seven "Millennium Prize Problems." These are the seven most notorious unsolved problems in mathematics, and guess what, a correct solution to each comes with a reward of $1 million! The problems were established by the Clay Mathematics Institute in 2000.

The problems are:

1. Birch and Swinnerton-Dyer Conjecture

2. Hodge Conjecture

3. Navier–Stokes Existence and Smoothness

4. P versus NP Problem

5. Poincaré Conjecture (solved in 2003 by Grigori Perelman)

6. Riemann Hypothesis

7. Yang–Mills Existence and Mass Gap.

While they are extremely advanced and generally require knowledge far beyond high school mathematics, they can serve as a fun way to see just how complex and rich the field of mathematics is.

For problems that are a bit more tractable, you might be interested in the difficulty levels of problems on the American Mathematical Society's annual competition, the "Putnam Exam." It's considered one of the toughest maths competitions for undergraduates, but the problems can certainly be a fun challenge for a motivated high school student.

Best of luck with your explorations into the world of complex mathematics!