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  2. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    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.

  3. List of undecidable problems - Wikipedia

    en.wikipedia.org/wiki/List_of_undecidable_problems

    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 .

  4. Category:Unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/Category:Unsolved_problems...

    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.

  5. Hilbert's problems - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_problems

    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

  6. Lists of unsolved problems - Wikipedia

    en.wikipedia.org/wiki/Lists_of_unsolved_problems

    List of unsolved problems may refer to several notable conjectures or open problems in various ... Unsolved problems in information theory; Social sciences and ...

  7. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    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 ...

  8. Smale's problems - Wikipedia

    en.wikipedia.org/wiki/Smale's_problems

    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.

  9. Union-closed sets conjecture - Wikipedia

    en.wikipedia.org/wiki/Union-closed_sets_conjecture

    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.