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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.
For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [5] the zeroes of a function; whether the indefinite integral of a function is also in the class. [6] Of course, some subclasses of these problems are decidable.
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine [ edit ]
Problems 1, 2, 5, 6, [g] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis ), 13 and 16 [ h ] unresolved, and 4 and 23 as too vague to ever be described as solved.
In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distance 1 from each other have the same color. The answer is unknown, but has been narrowed down to one of the numbers 5, 6 or 7.
The other six Millennium Prize Problems remain unsolved, despite a large number of unsatisfactory proofs by both amateur and professional mathematicians. Andrew Wiles , as part of the Clay Institute's scientific advisory board, hoped that the choice of US$ 1 million prize money would popularize, among general audiences, both the selected ...
In 1936, Erdős and Turán made the weaker conjecture that any set of integers with positive natural density contains infinitely many 3 term arithmetic progressions. [1] This was proven by Klaus Roth in 1952, and generalized to arbitrarily long arithmetic progressions by Szemerédi in 1975 in what is now known as Szemerédi's theorem .
This category is intended for all unsolved problems in mathematics, including conjectures. Conjectures are qualified by having a suggested or proposed hypothesis. There may or may not be conjectures for all unsolved problems.