Frequently Asked Questions

Unsolved math problems are mathematical questions that have not yet been proven or disproven despite extensive research by mathematicians worldwide. These problems exist across all branches of mathematics including:

• Number Theory: Prime numbers, divisibility, Diophantine equations
• Algebra: Polynomial equations, group theory, ring theory
• Geometry: Topology, manifolds, geometric constructions
• Combinatorics: Graph theory, counting problems, optimization
• Analysis: Differential equations, infinite series, functions

Famous examples include the Riemann Hypothesis, P vs NP, Goldbach's conjecture, and the Collatz conjecture.

One of the oldest unsolved problems is the Twin Prime Conjecture, proposed by Euclid around 300 BCE. It states that there are infinitely many prime numbers p such that p + 2 is also prime.

Other ancient unsolved problems include:

• Goldbach's conjecture (1742) - Every even integer greater than 2 is the sum of two primes
• Perfect numbers (ancient Greece) - Numbers equal to the sum of their proper divisors

The exact number of unsolved mathematical problems is unknown and possibly infinite, as new problems are proposed regularly by mathematicians around the world.

OpenMystery currently tracks thousands of documented unsolved problems across multiple branches of mathematics. Some estimates suggest there may be millions of open problems in mathematics, though many are highly specialized and narrow in scope.

The 7 millennium prize problems were selected by the Clay Mathematics Institute in 2000, each offering a $1 million prize for a correct solution:

1. P vs NP - Is every problem whose solution can be quickly verified also quickly solvable?
2. Hodge conjecture - Technical problem in algebraic geometry
3. Riemann hypothesis - Pattern in the distribution of prime numbers
4. Yang-Mills existence and mass gap - Quantum physics and mathematics
5. Navier-Stokes existence and smoothness - Fluid dynamics equations
6. Birch and Swinnerton-Dyer conjecture - Elliptic curves and rational points
7. Poincaré conjecture - Properties of 3-dimensional spheres (PROVEN by Grigori Perelman in 2003)

As of now, AI systems have not solved any major unsolved mathematical problems. While AI excels at:

• Pattern recognition and data analysis
• Computational verification of conjectures
• Exploring large solution spaces
• Assisting with routine calculations

However, solving landmark unsolved problems typically requires:

• Deep conceptual insights and creative leaps
• Novel mathematical frameworks
• Intuition about abstract structures

OpenMystery tracks AI attempt history on these problems to understand where AI approaches fail and what patterns emerge.

The most famous unsolved problems in mathematics include:

• Goldbach's conjecture (1742) - Every even integer greater than 2 is the sum of two primes
• Twin prime conjecture - Infinitely many twin primes exist
• Collatz conjecture - A simple sequence that always reaches 1
• Riemann hypothesis - Pattern in prime number distribution ($1 million prize)
• P vs NP - Are problems easy to verify also easy to solve? ($1 million prize)
• 孪生素数猜想 - Related to gaps between prime numbers

These problems are notable because they are simple to state but extraordinarily difficult to prove.

Unsolved algebra problems span various areas including:

• Polynomial equations: The Jacobian conjecture, Hilbert's 16th problem
• Group theory: The Burnside problem, classification of finite simple groups extensions
• Ring theory: The Kurosh problem, zero divisor questions
• Field theory: The inverse Galois problem
• Linear algebra: The determinant problem, permanent vs. hafnian

Browse our collection of unsolved algebra problems →

A list of unsolved math problems is a compilation of mathematical conjectures and hypotheses that have not yet been proven or disproven. OpenMystery provides a comprehensive database including:

• Problems by field (number theory, algebra, geometry, etc.)
• Problems by difficulty level
• Problems with AI attempt history
• The 7 Millennium Prize Problems ($1 million each)