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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); [4] the zeroes of a function; whether the indefinite integral of a function is also in the class. [5] Of course, some subclasses of these problems are decidable.
The end of the millennium, which was also the centennial of Hilbert's announcement of his problems, provided a natural occasion to propose "a new set of Hilbert problems". Several mathematicians accepted the challenge, notably Fields Medalist Steve Smale , who responded to a request by Vladimir Arnold to propose a list of 18 problems ( Smale's ...
In other projects Wikidata item; ... List of unsolved problems may refer to several notable conjectures or open problems in ... Unsolved problems in information theory;
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 ...
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems verifiable in polynomial time by a deterministic Turing machine. The first definition is the basis for the abbreviation NP; "nondeterministic, polynomial time". These two definitions are equivalent because the ...
This project was set up in order to try to solve the Erdős discrepancy problem. It was active for much of 2010 and had a brief revival in 2012, but did not end up solving the problem. However, in September 2015, Terence Tao, one of the participants of Polymath5, solved the problem in a pair of papers. One paper proved an averaged form of the ...