Editing List of theorems called fundamental

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In [[mathematics]], a '''fundamental theorem''' is a [[theorem]] which is considered to be central and conceptually important for some topic. For example, the [[fundamental theorem of calculus]] gives the relationship between [[differential calculus]] and [[integral calculus]].<ref>{{Citation | last1=Apostol | first1=Tom M. | author1-link=Tom M. Apostol | title=Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra | publisher=[[John Wiley & Sons]] | location=New York | edition=2nd | isbn=978-0-471-00005-1 | year=1967 | url-access=registration | url=https://archive.org/details/calculus01apos }}</ref> The names are mostly traditional, so that for example the [[fundamental theorem of arithmetic]] is basic to what would now be called [[number theory]].<ref>{{Hardy and Wright}}</ref> Some of these are [[Classification theorem|classification theorems]] of objects which are mainly dealt with in the field. For instance, the [[fundamental theorem of curves]] describes classification of [[Regular curve|regular curves]] in space up to [[Translation (geometry)|translation]] and [[rotation]].

Likewise, the mathematical literature sometimes refers to the '''fundamental lemma''' of a field. The term [[lemma (mathematics)|lemma]] is conventionally used to denote a proven proposition which is used as a stepping stone to a larger result, rather than as a useful statement in-and-of itself.

==Fundamental theorems of mathematical topics==
* [[Fundamental theorem of algebra]]
* [[Fundamental theorem of algebraic K-theory]]
* [[Fundamental theorem of arithmetic]]
* [[Fundamental theorem of Boolean algebra]]
* [[Fundamental theorem of calculus]]
* [[Fundamental theorem of calculus for line integrals]]
* [[Fundamental theorem of curves]]
* [[Fundamental theorem of cyclic groups]]
* [[Conley's fundamental theorem of dynamical systems|Fundamental theorem of dynamical systems]]
* [[Fundamental theorem of equivalence relations]]
* [[Fundamental theorem of exterior calculus]]
* [[Fundamental theorem of finitely generated abelian groups]]
* [[Fundamental theorem of finitely generated modules over a principal ideal domain]]
* [[Fundamental theorem of finite distributive lattices]]
* [[Fundamental theorem of Galois theory]]
* [[Fundamental theorem of geometric calculus]]
* [[Fundamental theorem on homomorphisms]]
* [[Fundamental theorem of ideal theory in number fields]]
* [[Fundamental theorem of Lebesgue integral calculus]]
* [[Fundamental theorem of linear algebra]]
* [[Fundamental theorem of linear programming]]
* [[Fundamental theorem of noncommutative algebra]]
* [[Fundamental theorem of projective geometry]]
* [[Fundamental theorem of random fields]]
* [[Fundamental theorem of Riemannian geometry]]
* [[Fundamental theorem of tessarine algebra]]
* [[Fundamental theorem of symmetric polynomials]]
* [[Fundamental theorem of topos theory]]
* [[Fundamental theorem of ultraproducts]]
* [[Fundamental theorem of vector analysis]]
[[Carl Friedrich Gauss]] referred to the law of [[quadratic reciprocity]] as the "fundamental theorem" of [[quadratic residue]]s.<ref>{{Cite journal|last=Weintraub|first=Steven H.|date=2011|title=On Legendre's Work on the Law of Quadratic Reciprocity|journal=[[The American Mathematical Monthly]]|volume=118|issue=3|pages=210|doi=10.4169/amer.math.monthly.118.03.210|s2cid=12076544}}</ref>

==Applied or informally stated "fundamental theorems"==
There are also a number of "fundamental theorems" that are not directly related to mathematics:
* [[Fundamental theorem of arbitrage-free pricing]]
* [[Fisher's fundamental theorem of natural selection]]
* [[Fundamental theorems of welfare economics]]
* [[Fundamental equations of thermodynamics]]
* [[Fundamental theorem of poker]]
* [[Holland's schema theorem]], or the "fundamental theorem of [[genetic algorithm]]s"
* [[Glivenko–Cantelli theorem]], or the "fundamental theorem of statistics"
* [[Fundamental theorem of software engineering]]

== Fundamental lemmata ==

* [[Fundamental lemma of the calculus of variations]]
* [[Fundamental lemma of Langlands and Shelstad]]
* [[Fundamental lemma of sieve theory]]

== See also ==
*[[Main theorem of elimination theory]]
*[[List of theorems]]
*[[Toy theorem]]

==References==
{{reflist}}

==External links==
*{{Commons category-inline|Fundamental theorems}}
*[https://arxiv.org/abs/1807.08416 "Some Fundamental Theorems in Mathematics" (Knill, 2018)] - self-described "expository hitchhikers guide", or exploration, of around 130 fundamental/influential mathematical results and their significance, across a range of mathematical fields.

[[Category:Mathematics-related lists|Theorems,Fundamental]]
[[Category:Theorems|Fundamental]]

[[es:Teorema fundamental]]
[[ka:ფუნდამენტური თეორემა]]