However, a generalization called the smooth four-dimensional Poincaré conjecture-that is, whether a four-dimensional topological sphere can have two or more inequivalent smooth structures-is unsolved. The seventh problem, the Poincaré conjecture, was solved by Grigori Perelman in 2003. Of the original seven Millennium Prize Problems listed by the Clay Mathematics Institute in 2000, six remain unsolved to date: The Riemann zeta function, subject of the celebrated and influential unsolved problem known as the Riemann hypothesis Millennium Prize Problems

Unsolved Problems on Mathematics for the 21st Century In some cases, the lists have been associated with prizes for the discoverers of solutions. Various mathematicians and organizations have published and promoted lists of unsolved mathematical problems. Lists of unsolved problems in mathematics Although this list may never be comprehensive, the problems listed here vary widely in both difficulty and importance. This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative. Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention. Some problems belong to more than one discipline and are studied using techniques from different areas. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Many mathematical problems have been stated but not yet solved. You can help by adding missing items with reliable sources. This is a dynamic list and may never be able to satisfy particular standards for completeness.

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