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  2. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Bolzano's theorem (real analysis, calculus) Bolzano–Weierstrass theorem (real analysis, calculus) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Bondareva–Shapley theorem ; Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Bonnet theorem (differential geometry)

  3. List of conjectures - Wikipedia

    en.wikipedia.org/wiki/List_of_conjectures

    ⇐Faltings's theorem, the Shafarevich conjecture on finiteness of isomorphism classes of abelian varieties. The reduction step was by Alexey Parshin. 1983 onwards: Neil Robertson and Paul D. Seymour: Wagner's conjecture: graph theory: Now generally known as the graph minor theorem. 1983: Michel Raynaud: Manin–Mumford conjecture: diophantine ...

  4. 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 ...

  5. Proof assistant - Wikipedia

    en.wikipedia.org/wiki/Proof_assistant

    In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface , with which a human can guide the search for proofs, the details of which are ...

  6. List of incomplete proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_incomplete_proofs

    For example, a Fourier series of sine and cosine functions, all continuous, may converge pointwise to a discontinuous function such as a step function. Carmichael's totient function conjecture was stated as a theorem by Robert Daniel Carmichael in 1907, but in 1922 he pointed out that his proof was incomplete. As of 2016 the problem is still open.

  7. Computer-assisted proof - Wikipedia

    en.wikipedia.org/wiki/Computer-assisted_proof

    Computer-assisted proofs are the subject of some controversy in the mathematical world, with Thomas Tymoczko first to articulate objections. Those who adhere to Tymoczko's arguments believe that lengthy computer-assisted proofs are not, in some sense, 'real' mathematical proofs because they involve so many logical steps that they are not practically verifiable by human beings, and that ...

  8. Faltings's theorem - Wikipedia

    en.wikipedia.org/wiki/Faltings's_theorem

    Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field of rational numbers has only finitely many rational points. This was conjectured in 1922 by Louis Mordell, [1] and known as the Mordell conjecture until its 1983 proof by Gerd Faltings. [2]

  9. Hilbert system - Wikipedia

    en.wikipedia.org/wiki/Hilbert_system

    In logic, more specifically proof theory, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of formal proof system attributed to Gottlob Frege [1] and David Hilbert. [2]

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