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  2. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    P. Oxy. 29, one of the oldest surviving fragments of Euclid's Elements, a textbook used for millennia to teach proof-writing techniques. The diagram accompanies Book II, Proposition 5. [1] A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the

  3. List of mathematical proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_proofs

    Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges

  4. List of incomplete proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_incomplete_proofs

    The proof was completed by Werner Ballmann about 50 years later. Littlewood–Richardson rule. Robinson published an incomplete proof in 1938, though the gaps were not noticed for many years. The first complete proofs were given by Marcel-Paul Schützenberger in 1977 and Thomas in 1974. Class numbers of imaginary quadratic fields.

  5. Langley's Adventitious Angles - Wikipedia

    en.wikipedia.org/wiki/Langley's_Adventitious_Angles

    In 2015, an anonymous Japanese woman using the pen name "aerile re" published the first known method (the method of 3 circumcenters) to construct a proof in elementary geometry for a special class of adventitious quadrangles problem. [7] [8] [9] This work solves the first of the three unsolved problems listed by Rigby in his 1978 paper. [5]

  6. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures

  7. Foundations of geometry - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_geometry

    Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.

  8. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime numbers. This was Hilbert's eighth problem, and is still considered an important open problem a century later. The problem has been well-known ever since it was originally posed by Bernhard Riemann in 1860.

  9. Carathéodory conjecture - Wikipedia

    en.wikipedia.org/wiki/Carathéodory_conjecture

    The local real analytic version of the conjecture has had a troubled history with published proofs [13] [14] which contained gaps. [15] The proof for smooth surfaces by Brendan Guilfoyle and Wilhelm Klingenberg, first announced in 2008, [16] was published in three parts [17] [18] [19] concluding in 2024, the centenary of the conjecture. Their ...

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