- Goldbach's Conjecture
Since the 1995 proof of Fermat's Last Theorem, a problem which stood for 365 years, the current longest-standing maths problem is the conjecture posed by Christian Goldbach (1690-1764), a Russian mathematician, in 1742. Goldbach's Conjecture states that every even positive integer greater than 3 is the sum of two (not necessarily distinct) primes. No one has succeeded in proving or disproving the validity of this conjecture in 257 years.
Mathematicians worldwide hold the Riemann Hypothesis of 1859 (posed by German mathematician Bernhard Riemann (1826-1866)) as the most important outstanding maths problem. The hypothesis states that all nontrivial roots of the Zeta function are of the form (1/2 + b I).