**This is a nice list of famous unsolved math problems from Wolfram MathWorld:**

http://mathworld.wolfram.com/UnsolvedProblems.html

There are some well-known problems here, like the Goldbach Conjecture and the Collatz Conjecture, and some lesser-known open problems like finding an Euler Brick with an integral space diagonal.

It’s especially nice that several of these challenges are easy to explain to non-mathematicians. For example, the Goldbach Conjecture asks “*Can every even number be written as the sum of two prime numbers?*” Somewhat surprisingly, after nearly 300 years, the best answer we have is probably.

I think I’ll make this page next year’s summer homework assignment.