Open Problems
Millennium prizes, quantum gravity, turbulence — where equations still hide secrets.
- Unsolved
Navier-Stokes Existence and Smoothness
Do smooth solutions always exist in 3D? Millennium Prize problem.
- Unsolved
Yang-Mills Mass Gap
Prove quantum Yang-Mills theory has a mass gap.
- Unsolved
Riemann Hypothesis
All non-trivial zeros of ζ(s) lie on Re(s)=1/2.
- Open research
Quantum Gravity
Unify general relativity with quantum mechanics.
- Observational mystery
Dark Matter
What is the nature of dark matter?
- Partially understood
Turbulence
Complete statistical theory of turbulent flow.
- Computational challenge
Protein Folding
Predict 3D structure from amino acid sequence.
- Active research
Climate Uncertainty
Reduce uncertainty in long-term climate projections.