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  2. List of mathematical theories - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_theories

    Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...

  3. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Bass-Guirvarc'h formula (group theory) Bass-Serre theorem (group theory) Basu's theorem ; Bauer–Fike theorem (spectral theory) Bayes' theorem (probability) Beatty's theorem (Diophantine approximation) Beauville–Laszlo theorem (vector bundles) Beck's monadicity theorem (category theory) Beck's theorem (incidence geometry)

  4. List of mathematical proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_proofs

    Fundamental theorem of Galois theory (to do) Gödel number. Gödel's incompleteness theorem; Group (mathematics) Halting problem. insolubility of the halting problem; Harmonic series (mathematics) divergence of the (standard) harmonic series; Highly composite number; Area of hyperbolic sector, basis of hyperbolic angle; Infinite series

  5. List of conjectures - Wikipedia

    en.wikipedia.org/wiki/List_of_conjectures

    number theory: Dorin Andrica: 45 Artin conjecture (L-functions) number theory: Emil Artin: 650 Artin's conjecture on primitive roots: number theory: ⇐generalized Riemann hypothesis [2] ⇐Selberg conjecture B [3] Emil Artin: 325 Bateman–Horn conjecture: number theory: Paul T. Bateman and Roger Horn: 245 Baum–Connes conjecture: operator K ...

  6. List of first-order theories - Wikipedia

    en.wikipedia.org/wiki/List_of_first-order_theories

    The theory of an equivalence relation with exactly 2 infinite equivalence classes is an easy example of a theory which is ω-categorical but not categorical for any larger cardinal. The equivalence relation ~ should not be confused with the identity symbol '=': if x=y then x~y, but the converse is not necessarily true. Theories of equivalence ...

  7. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones. This definition makes the concept of proof amenable to study.

  8. List of theorems called fundamental - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems_called...

    For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus. [1] The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory . [ 2 ]

  9. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    [117] [118] Many of the theories developed for applications were found interesting from the point of view of pure mathematics, and many results of pure mathematics were shown to have applications outside mathematics; in turn, the study of these applications may give new insights on the "pure theory". [119] [120] An example of the first case is ...

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