Search results
Results from the WOW.Com Content Network
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.
Download as PDF; Printable version; ... Unsolved problems in neuroscience; ... Unsolved problems in information theory; Social sciences and humanities
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 computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set ; see the article Decidable language .
This category is intended for all unsolved problems in mathematics, including conjectures. Conjectures are qualified by having a suggested or proposed hypothesis. Conjectures are qualified by having a suggested or proposed hypothesis.
Szemerédi's theorem states that a set of natural numbers of non-zero upper asymptotic density contains finite arithmetic progressions, of any arbitrary length k. Erdős made a more general conjecture from which it would follow that The sequence of primes numbers contains arithmetic progressions of any length.
Secondly, we show that if a set system contains an element in at least half the sets, then its complement has an element in at most half. Lemma 2. A set system contains an element in half of its sets if and only if the complement set system , contains an element in at most half of its sets. Proof.
The Beal conjecture is the following conjecture in number theory: Unsolved problem in mathematics : If A x + B y = C z {\displaystyle A^{x}+B^{y}=C^{z}} where A , B , C , x , y , z are positive integers and x , y , z are ≥ 3, do A , B , and C have a common prime factor?