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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.
Proven to be impossible to prove or disprove within Zermelo–Fraenkel set theory with or without the axiom of choice (provided Zermelo–Fraenkel set theory is consistent, i.e., it does not contain a contradiction). There is no consensus on whether this is a solution to the problem. 1940, 1963 2nd
List of unsolved problems may refer to several notable conjectures or open problems in various ... Unsolved problems in information theory; Social sciences and ...
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 geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact-dimensional spaces. Intuitively, it states that a set of points that is large in its Hausdorff dimension must determine a set of distances that is large in measure .
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 .
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 ...
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.