I love mathematics too. I hope to one day solve the Traveling Salesman problem and find a perfect cuboid.

What is the Traveling Salesman problem?

If you have N cities, points, or whatever, and you know the distance between every two, find the shortest path that visits every one and returns to the point of origin. There is no known less-than-exponential algorithm that is guaranteed to give the optimal solution, and thus it is computationally infeasible to find the optimal solution for more than a relatively small number of cities. There are heuristic algorithms that can find a pretty good solution for many more cities in far less computation time but it's not guaranteed to be optimal.

The perfect cubiod problem is to find a brick with the property that the distance between every two vertices is an integer. If every two edges forms a Pythagorean triple with the corresponding face diagonal, it's a Euler brick, and there are many solutions known, but none have been found where the space diagonal is also an integer, nor has anyone been able to prove that none exists.