Unsolved Math Problems

We've all been stumped by math problems before. Sometimes it takes a while for a method or equation to click. But with practice and help, it eventually does. However, there are some math problems that has left the world collectively scratching their heads, some for over 100 years! Here is a list of some of the most complicated, unsolved math problems the world has ever seen:

1. Goldbach Conjecture: Goldbach asserts that all positive even integers >=4 can be expressed as the sum of two primes. Two primes (p,q) such that p+q=2n for n a positive integer are sometimes called a Goldbach partition (Oliveira e Silva).
2. Riemann Hypothesis:  neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2.
3. Twin prime conjecture: the conjecture that there are an infinite number of twin primes
4. The 196-algorithm: proof that the 196-algorithm does not terminate when applied to the number 196
5. Proof that 10 is a solitary number: A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers; some numbers can be proved not to be solitary by finding another integer with the same index, although sometimes the smallest such number is fairly large;  a proof appears to be extremely difficult
6. Determining if any odd perfect numbers exist: Perfect numbers are positive integers n such that n = s(n), where s(n) is the restricted divisor function (i.e., the sum of proper divisors of n), or equivalently sigma(n)=2n, where sigma (n) is the divisor function (i.e., the sum of divisors of n including n itself); for example, the first few perfect numbers are 6, 28, 496, 8128

           Ex.) 6 = 1 + 2 + 3
           Ex.) 28 = 1 + 2 + 4 + 7 + 14
           Ex.) 496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248

(Source: Wolfram MathWorld)