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  2. Conjecture - Wikipedia

    en.wikipedia.org/wiki/Conjecture

    In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to ...

  3. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    Although not a formal proof, a visual demonstration of a mathematical theorem is sometimes called a "proof without words". The left-hand picture below is an example of a historic visual proof of the Pythagorean theorem in the case of the (3,4,5) triangle.

  4. James W. Cannon - Wikipedia

    en.wikipedia.org/wiki/James_W._Cannon

    The conjecture (Conjecture 5.1 in [29]) states that if the ideal boundary of a word-hyperbolic group G is homeomorphic to the 2-sphere, then G admits a properly discontinuous cocompact isometric action on the hyperbolic 3-space (so that G is essentially a 3-dimensional Kleinian group).

  5. Category:Conjectures - Wikipedia

    en.wikipedia.org/wiki/Category:Conjectures

    A conjecture is a proposition that is unproven. Conjectures are related to hypotheses , which in science are empirically testable conjectures. In mathematics , a conjecture is an unproven proposition that appears correct.

  6. Cramér's conjecture - Wikipedia

    en.wikipedia.org/wiki/Cramér's_conjecture

    In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, [1] is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be. It states that

  7. List of conjectures - Wikipedia

    en.wikipedia.org/wiki/List_of_conjectures

    As reformulated, it became the "paving conjecture" for Euclidean spaces, and then a question on random polynomials, in which latter form it was solved affirmatively. 2015: Jean Bourgain, Ciprian Demeter, and Larry Guth: Main conjecture in Vinogradov's mean-value theorem: analytic number theory: Bourgain–Demeter–Guth theorem, ⇐ decoupling ...

  8. Landau's problems - Wikipedia

    en.wikipedia.org/wiki/Landau's_problems

    Goldbach's weak conjecture, every odd number greater than 5 can be expressed as the sum of three primes, is a consequence of Goldbach's conjecture. Ivan Vinogradov proved it for large enough n (Vinogradov's theorem) in 1937, [1] and Harald Helfgott extended this to a full proof of Goldbach's weak conjecture in 2013. [2] [3] [4]

  9. Dejean's theorem - Wikipedia

    en.wikipedia.org/wiki/Dejean's_theorem

    Dejean's theorem (formerly Dejean's conjecture) is a statement about repetitions in infinite strings of symbols. It belongs to the field of combinatorics on words ; it was conjectured in 1972 by Françoise Dejean and proven in 2009 by Currie and Rampersad and, independently, by Rao.