07-06-2026, 08:32 PM
List of unsolved problems in mathematics
Summary
The history of mathematics is filled with famous problems that resisted solution for decades or even centuries, and this list highlights many of the most important ones that remain open today. It brings together outstanding questions from virtually every branch of mathematics—including number theory, algebra, geometry, topology, graph theory, analysis, dynamical systems, set theory, and computer science—ranging from deceptively simple puzzles to deep conjectures with far-reaching consequences. Among the best-known are the six remaining Millennium Prize Problems, such as the Riemann hypothesis, P versus NP problem, and the Navier–Stokes existence and smoothness, each carrying a $1 million prize for a correct solution.
The article also places these problems in historical context by referencing influential collections such as Hilbert's problems, Landau's problems, Smale's problems, and the thousands of questions posed by Paul Erdős. Together, these unsolved problems illustrate that mathematics is a living and evolving discipline, where every major breakthrough not only answers long-standing questions but often opens the door to entirely new areas of discovery.
ARTICLE
Summary
The history of mathematics is filled with famous problems that resisted solution for decades or even centuries, and this list highlights many of the most important ones that remain open today. It brings together outstanding questions from virtually every branch of mathematics—including number theory, algebra, geometry, topology, graph theory, analysis, dynamical systems, set theory, and computer science—ranging from deceptively simple puzzles to deep conjectures with far-reaching consequences. Among the best-known are the six remaining Millennium Prize Problems, such as the Riemann hypothesis, P versus NP problem, and the Navier–Stokes existence and smoothness, each carrying a $1 million prize for a correct solution.
The article also places these problems in historical context by referencing influential collections such as Hilbert's problems, Landau's problems, Smale's problems, and the thousands of questions posed by Paul Erdős. Together, these unsolved problems illustrate that mathematics is a living and evolving discipline, where every major breakthrough not only answers long-standing questions but often opens the door to entirely new areas of discovery.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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