Unsolved Problems (1)
The most famous unsolved problem in Mathematics is probably the Riemann Hypothesis, which I've never really got my head around.
But there are other unproven conjectures and hypotheses out there which are easily understood.
For instance, Goldbach’s Conjecture, (1742), states that every even number greater than 2 can be expressed as the sum of two primes.
For example: 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5 and so on.
It’s been tested and found to be true for all even numbers up to 400000000000000 but nobody so far has proved that it’s true for all even numbers greater than 2.