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  2. Continuum hypothesis - Wikipedia

    en.wikipedia.org/wiki/Continuum_hypothesis

    Cohen [4] [7] showed that CH cannot be proven from the ZFC axioms, completing the overall independence proof. To prove his result, Cohen developed the method of forcing, which has become a standard tool in set theory. Essentially, this method begins with a model of ZF in which CH holds, and constructs another model which contains more sets than ...

  3. Doomsday conjecture - Wikipedia

    en.wikipedia.org/wiki/Doomsday_conjecture

    In algebraic topology, the doomsday conjecture was a conjecture about Ext groups over the Steenrod algebra made by Joel Cohen, named by Michael Barratt, published by Milgram (1971, conjecture 73) and disproved by Mahowald (1977). Minami (1995) stated a modified version called the new doomsday conjecture.

  4. Homological conjectures in commutative algebra - Wikipedia

    en.wikipedia.org/wiki/Homological_conjectures_in...

    Then there exists an R-algebra B R that is a balanced big Cohen–Macaulay algebra for R, an S-algebra that is a balanced big Cohen-Macaulay algebra for S, and a homomorphism B R → B S such that the natural square given by these maps commutes. Serre's Conjecture on Multiplicities. (cf. Serre's multiplicity conjectures.

  5. Motivic cohomology - Wikipedia

    en.wikipedia.org/wiki/Motivic_cohomology

    This is one of the central problems of number theory, incorporating earlier conjectures by Deligne and Beilinson. The Birch–Swinnerton-Dyer conjecture is a special case. More precisely, the conjecture predicts the leading coefficient of the L-function at an integer point in terms of regulators and a height pairing on motivic cohomology.

  6. Occam's razor - Wikipedia

    en.wikipedia.org/wiki/Occam's_razor

    In philosophy, Occam's razor (also spelled Ockham's razor or Ocham's razor; Latin: novacula Occami) is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements.

  7. Standard conjectures on algebraic cycles - Wikipedia

    en.wikipedia.org/wiki/Standard_conjectures_on...

    The Hodge standard conjecture is not to be confused with the Hodge conjecture which states that for smooth projective varieties over C, every rational (p, p)-class is algebraic. The Hodge conjecture implies the Lefschetz and Künneth conjectures and conjecture D for varieties over fields of characteristic zero.

  8. Brown–Gitler spectrum - Wikipedia

    en.wikipedia.org/wiki/Brown–Gitler_spectrum

    In topology, Brown–Gitler spectrum is related to the concepts of the Segal conjecture (proven in 1984) and the Burnside ring. [4] Applications.

  9. Richard Borcherds - Wikipedia

    en.wikipedia.org/wiki/Richard_Borcherds

    Richard Ewen Borcherds (/ ˈ b ɔːr tʃ ər d z /; born 29 November 1959) [2] is a British [4] mathematician currently working in quantum field theory.He is known for his work in lattices, group theory, and infinite-dimensional algebras, [5] [6] for which he was awarded the Fields Medal in 1998.