What are the 7 unsolved mathematics problems?

The seven Millennium Prize Problems, established by the Clay Mathematics Institute in 2000, are: P vs NP, Hodge Conjecture, Riemann Hypothesis, Yang-Mills Existence, Navier-Stokes Existence, Birch and Swinnerton-Dyer Conjecture, and Poincaré Conjecture (solved in 2003).

The Millennium Prize Problems ($1 million each):

1. P vs NP Problem: Can every problem whose solution can be quickly verified also be quickly solved?
2. Hodge Conjecture: Relationship between algebraic geometry and topology
3. Riemann Hypothesis: Distribution of prime numbers
4. Yang-Mills Existence and Mass Gap: Quantum field theory foundations
5. Navier-Stokes Existence and Smoothness: Fluid dynamics equations
6. Birch and Swinnerton-Dyer Conjecture: Elliptic curves and number theory
7. Poincaré Conjecture: ✓ SOLVED by Grigori Perelman (2003)

Why These Matter:

• Each has profound implications for mathematics and science
• Solutions could revolutionize computing, physics, or engineering
• They represent fundamental gaps in mathematical understanding

Important Notes:

• Only one has been solved (Poincaré Conjecture)
• Each problem is extraordinarily difficult
• Solutions require groundbreaking insights
• Progress continues on multiple fronts