Unsolved Problems
Goldbach's
Conjecture. This had a $1,000,000.00 prize associated with it!
Twin Prime's
Conjecture
Does there exist an odd perfect number. A perfect number is the sum of its
proper divisors (e.g. 1+2+3=6). This was posed by Euclid, and is still open.
Here is a list of
Unsolved Problems some of which are very geometric in nature.
Some
unsolved conjectures involving primes.
Some
open problems in geomtry.
Seven problems, each of which will get you $1,000,000.00 if you solve
it! Each of them have a video (in Real Media format) of approximately
one hour, as well as an official description of the problem.
A list of
17 unsolved problems and links [from MathWorld]
Another general list
of mathematical problems.
A list of Open
Problems [undergraduate level mathematics]
Good Luck!