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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.
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.
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine [ edit ]
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.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help ... Category: Unsolved problems in number theory.
(more unsolved problems in mathematics) Erdős' conjecture on arithmetic progressions can be viewed as a stronger version of Szemerédi's theorem. Because the sum of the reciprocals of the primes diverges, the Green–Tao theorem on arithmetic progressions is a special case of the conjecture.
The kernel of the sunflower is the brown part in the middle, and each set of the sunflower is the union of a petal and the kernel. In the mathematical fields of set theory and extremal combinatorics, a sunflower or -system [1] is a collection of sets in which all possible distinct pairs of sets share the same intersection.
The Erdős–Straus conjecture is one of many conjectures by Erdős, and one of many unsolved problems in mathematics concerning Diophantine equations. Although a solution is not known for all values of n , infinitely many values in certain infinite arithmetic progressions have simple formulas for their solution, and skipping these known values ...