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Many mathematical problems have been stated but not yet solved. 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.
Pages in category "Unsolved problems in number theory" The following 106 pages are in this category, out of 106 total. This list may not reflect recent changes .
Find the most general law of the reciprocity theorem in any algebraic number field. Partially resolved. Solved by Emil Artin in 1927 for Abelian extensions of the rational numbers during the development of class field theory. The non-abelian case remains unsolved, if one interprets that as meaning non-abelian class field theory. — 10th
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold for all integers less than 4 × 10 18 but remains unproven despite considerable effort.
Traditionally, number theory is the branch of mathematics concerned with the properties of integers and many of its open problems are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arise naturally from the study of integers.
The result has caught the imagination of most mathematicians because it is so unexpected, connecting two seemingly unrelated areas in mathematics; namely, number theory, which is the study of the discrete, and complex analysis, which deals with continuous processes. —
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
The class field theory concerns abelian extensions of number fields. class number 1. The class number of a number field is the cardinality of the ideal class group of the field. 2. In group theory, the class number is the number of conjugacy classes of a group. 3. Class number is the number of equivalence classes of binary quadratic forms of a ...
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