Millennium Prize Problems
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A Millennium Prize Problems is a mathematical problem set that consists of seven unsolved mathematical challenges selected by the Clay Mathematics Institute in 2000, each offering a one million dollar prize.
- AKA: Clay Millennium Problems, Millennium Problems, Million Dollar Problems.
- Context:
- It can typically address Fundamental Mathematical Questions with profound implications.
- It can typically stimulate Global Mathematical Research through monetary incentives.
- It can typically require Breakthrough Mathematical Insights for problem resolution.
- It can often influence Research Directions in mathematical communities.
- It can often generate Partial Results through incremental progress.
- It can range from being a Number Theory Millennium Prize Problem to being a Topology Millennium Prize Problem, depending on its mathematical domain.
- It can range from being a Computational Millennium Prize Problem to being a Theoretical Millennium Prize Problem, depending on its solution approach.
- It can range from being an Accessible Millennium Prize Problem to being a Highly Technical Millennium Prize Problem, depending on its comprehension difficulty.
- It can range from being a Nearly Solved Millennium Prize Problem to being a Completely Open Millennium Prize Problem, depending on its progress status.
- ...
- Example:
- Individual Millennium Prize Problems, such as:
- P versus NP Problem for computational complexity.
- Riemann Hypothesis for prime distribution.
- Navier-Stokes Singularity Problem for fluid dynamics.
- Yang-Mills Existence Problem for gauge theory.
- Hodge Conjecture for algebraic geometry.
- Birch and Swinnerton-Dyer Conjecture for elliptic curves.
- Poincaré Conjecture (solved by Grigori Perelman).
- ...
- Individual Millennium Prize Problems, such as:
- Counter-Example:
- Hilbert's Problems, which lack monetary prizes.
- Fields Medal Problem, which recognizes completed work rather than open problems.
- See: Mathematical Problem Set, Clay Mathematics Institute, Prize Problem, Unsolved Problem in Mathematics, Navier-Stokes Equation, Mathematical Research, Problem Solving Task.