Uniform boundedness conjecture for rational points.Existence of perfect cuboids and associated cuboid conjectures.Homological conjectures in commutative algebra.Grothendieck–Katz p-curvature conjecture.Finite lattice representation problem.
The Erlagol Notebook ( Erlagolskaya Tetrad) collects unresolved problems in algebra and model theory.The Dniester Notebook ( Dnestrovskaya Tetrad) collects several hundred unresolved problems in algebra, particularly ring theory and modulus theory.Zauner conjectured that analogous structures exist in complex Hilbert spaces of all finite dimensions. In the Bloch sphere representation of a qubit, a SIC-POVM forms a regular tetrahedron. 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 6.1 Books discussing problems solved since 1995.2.11.1 Conjectures, problems, and hypotheses.2.10.5.1 Conjectures, problems and hypotheses.2.10.1.1 Conjectures, problems and hypotheses.1 Lists of unsolved problems in mathematics.This list includes problems which are considered by the mathematical community to be widely varying in both difficulty and centrality to the science as a whole. The list is not comprehensive, for at least the reason that entries may not be updated at the time of viewing. This article is a composite of notable unsolved problems derived from many sources, including but not limited to lists considered authoritative. Prizes are often awarded for the solution to a long-standing problem, and lists of unsolved problems, such as the list of Millennium Prize Problems, receive considerable attention. Some problems may belong to more than one discipline of mathematics and be studied using techniques from different areas. These unsolved problems occur in multiple domains, including theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph, group, model, number, set and Ramsey theories, dynamical systems, and partial differential equations. Many mathematical problems have not yet been solved.
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