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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.
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 .
List of unsolved problems may refer to several notable conjectures or open problems in various ... Unsolved problems in information theory; Social sciences and ...
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 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 ...
Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer. For other problems, such as the 5th, experts have traditionally agreed on a single interpretation, and a solution to ...
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
An intersecting family of -element sets may be maximal, in that no further set can be added (even by extending the ground set) without destroying the intersection property, but not of maximum size. An example with n = 7 {\displaystyle n=7} and r = 3 {\displaystyle r=3} is the set of seven lines of the Fano plane , much less than the Erdős–Ko ...