Problems still waiting on a proof.

Does every problem whose solution can be verified quickly also admit a quick algorithm to find that solution? A decisive answer would redraw the map of computation, cryptography, and optimization.

Do all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2? The hypothesis governs the finest distribution of the prime numbers.

Produce a mathematically consistent framework that unifies quantum field theory with general relativity, recovering both in the appropriate limits and making sharp, testable predictions.

Do the three-dimensional incompressible Navier–Stokes equations always admit smooth, globally defined solutions — or can singularities form from smooth initial data?

Establish a rigorous quantum Yang–Mills theory on R⁴ and prove that it has a positive mass gap — the lowest excitation sits strictly above the vacuum.

Formulate and validate a general, predictive theory of how proteins fold and misfold in physiologically relevant conditions — beyond static structure prediction alone.

Are Hodge classes on a non-singular complex projective variety algebraic — that is, rational linear combinations of cohomology classes of algebraic subvarieties?

Are there infinitely many primes p such that p + 2 is also prime? Bounded-gap breakthroughs brought us close — the infinite twin-prime statement remains open.

Starting from any positive integer, repeatedly apply n → n/2 if even and n → 3n + 1 if odd. Does every trajectory eventually reach 1?