Fundamental theorem

In mathematics, there are a number of fundamental theorems for different fields. The names are mostly traditional; so that for example the "fundamental theorem of arithmetic" is basic to what would now be called number theory. Theorems may be called "fundamental" because they are results from which further, more complicated theorems follow, without reaching back to axioms. The mathematical literature will sometimes refer to the fundamental lemma of a field; this is often, but not always, the same as the fundamental theorem of that field.

"Fundamental Lemmas":

* fundamental lemma of calculus of variations
* fundamental lemma of Langlands and Shelstad

"Fundamental Theorems":

* fundamental theorem of algebra
* fundamental theorem of arithmetic
* fundamental theorem of calculus
* fundamental theorem of curves
* fundamental theorem of cyclic groups
* fundamental theorem of surfaces
* fundamental theorem of finitely generated abelian groups
* fundamental theorem of Galois theory
* fundamental theorem on homomorphisms
* fundamental theorem of linear algebra
* fundamental theorem of projective geometry
* fundamental theorem of Riemannian geometry
* fundamental theorem of vector analysis
* fundamental theorem of linear programming

There are also a number of fundamental theorems 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