There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include

1. The Goldbach conjecture.

2. The Riemann hypothesis.

3. The conjecture that there exists a Hadamard matrix for every positive multiple of 4.

4. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes).

5. Determination of whether NP-problems are actually P-problems.

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 S_n.

10. Solving the happy end problem for arbitrary n.

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.

13. Lehmer's Mahler measure problem and Lehmer's totient problem on the existence of composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function.

14. Determining if the Euler-Mascheroni constant is irrational.

15. Deriving an analytic form for the square site percolation threshold.

16. Determining if any odd perfect numbers exist.

The Clay Mathematics Institute ( [link to www.claymath.org] of Cambridge, Massachusetts (CMI) has named seven "Millennium Prize Problems," selected by focusing on important classic questions in mathematics that have resisted solution over the years. A $7 million prize fund has been established for the solution to these problems, with $1 million allocated to each. The problems consist of the Riemann hypothesis, Poincaré conjecture, Hodge conjecture, Swinnerton-Dyer Conjecture, solution of the Navier-Stokes equations, formulation of Yang-Mills theory, and determination of whether NP-problems are actually P-problems.