Unsolved mathematical problems I'm trying to figure out (along with flying, snowshoeing, and pig farming), but only in my dreams. 1. The Goldbach conjecture.
2. The Riemann hypothesis.
3. The conjecture that there exists a Hadamard matrix for every positive multiple of 4.
6. The Collatz problem.
7. Proof that the 196-algorithm does not terminate when applied to the number 196.
8. Proof that 10 is a solitary number.
9. Finding a formula for the probability that two elements chosen at random generate the symmetric group .
10. Solving the happy end problem for arbitrary .
11. Finding an Euler brick whose space diagonal is also an integer.
12. Proving which numbers can be represented as a sum of three or four (positive or negative) cubic numbers.
15. Deriving an analytic form for the square site percolation threshold.
16. Determining if any odd perfect numbers exist.