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  1. Theorem: A theorem is a statement that can be proven via logic which generally stems from a collection of postulates or axioms. They have been in use since Euclidean geometry as the basis of geometrical facts. [100%] 2023-02-21 [Mathematics]
  2. Theorem: In logic, a theorem is formally meant to be a formula that can be transformed by applying inferential rules to axioms in a deductive system. This formal notion of proofs in logic is crucial in fields such as proof theory ... [100%] 2023-02-03
  3. Theorem: In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a ... (In mathematics, a statement that has been proved) [100%] 2023-09-23 [Theorems] [Logical consequence]...
  4. Theorem: A mathematical statement whose truth has been established by means of a proof. The concept of a theorem developed and became more precise together with the concept of a mathematical proof. (Mathematics) [100%] 2023-10-18
  5. Group completion theorem: in algebraic topology Let $ M $ be a topological monoid and $ BM $ its classifying space. Let $ M \rightarrow \Omega BM $ be the canonical mapping. (Mathematics) [89%] 2023-12-28
  6. Serre theorem in group cohomology: A theorem proved by J.-P. Serre in 1965 about the cohomology of pro-$p$-groups which has important consequences in group cohomology and representation theory (cf. (Mathematics) [86%] 2023-09-17
  7. Theorum: Theorum (rhymes with decorum, apparently) is a neologism proposed by Richard Dawkins in The Greatest Show on Earth to distinguish the scientific meaning of theory from the colloquial meaning. In most of the opening introduction to the show, he substitutes ... [82%] 2024-01-05 [Neologisms] [Language]...
  8. Group theory: In mathematics, groups often arise as structures representing the set of possible symmetries of some object. We have been intentionally vague about the meaning of the terms symmetry and object. [81%] 2023-06-26
  9. Group theory: Group theory is the study of mathematical groups, including their symmetries and permutations. It has applications in science, and has become one of the most active branches in all of mathematics in the 20th century. [81%] 2023-03-13 [Algebra]
  10. Group theory: Welcome to Group Theory! Group Theory is a vibrant, wide area of current research in mathematics, computer science and mathematical/theoretical physics. [81%] 2024-01-19 [{{PAGENAME}}]
  11. Group theory: In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups ... (Branch of mathematics that studies the properties of groups) [81%] 2024-08-13 [Group theory]
  12. Fundamental theorem of Galois theory: In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions. In its most basic form, the theorem asserts that given a field extension E/F that is finite and ... [71%] 2023-11-03 [Field theory] [Theorems in group theory]...
  13. Fundamental theorem of topos theory: In mathematics, The fundamental theorem of topos theory states that the slice \displaystyle{ \mathbf{E} / X }[/math] of a topos \displaystyle{ \mathbf{E} }[/math] over any one of its objects \displaystyle{ X }[/math] is itself a topos. Moreover, if there ... [71%] 2023-11-03 [Topos theory]
  14. Seesaw theorem: In algebraic geometry, the seesaw theorem, or seesaw principle, says roughly that a limit of trivial line bundles over complete varieties is a trivial line bundle. It was introduced by André Weil in a course at the University of Chicago in ... [70%] 2023-10-20 [Abelian varieties]
  15. Frucht theorem: In 1938, R. Frucht affirmatively answered a question posed by D. (Mathematics) [70%] 2023-10-23
  16. Engel theorem: Suppose that for a finite-dimensional Lie algebra $ \mathfrak g $ over a field $ k $ the linear operators $$ \mathop{\rm ad} X \ ( \textrm{ where ad } X ( Y) = [ X , Y ] ) $$ are nilpotent for all $ X \in \mathfrak g $. Then there is a ... (Mathematics) [70%] 2023-10-25
  17. Shnirelman theorem: Shnirelman theorem refers to the asymptotic properties of eigenfunctions of the Schroedinger operator in case of a classically chaotic system. It says that for almost all eigenvalues the probability of finding the system in a vicinity of a given classical ... [70%] 2022-06-02 [Quantum Chaos]
  18. Rouché theorem: Let $f(z)$ and $g(z)$ be regular analytic functions (cf. Analytic function) of a complex variable $z$ in a domain $D$, let a simple closed piecewise-smooth curve $\Gamma$ together with the domain $G$ bounded by it belong to ... (Mathematics) [70%] 2023-10-20
  19. Vitali theorem: Vitali's covering theorem. If a system of closed sets $\mathcal F$ is a Vitali covering (see below) of a set $A\subset\mathbb R^n$, it is possible to extract from $\mathcal F$ an at most countable sequence of ... (Mathematics) [70%] 2023-10-23
  20. Meusnier theorem: If $\gamma$ is a curve lying on a surface and $P$ is a point on $\gamma$, then the curvature $k$ of $\gamma$ at $P$, the curvature $k_N$ of the normal section of the surface by the plane passing through both ... (Mathematics) [70%] 2023-10-17

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