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. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. ... In mathematics, a lemma is a proven proposition which is used as a stepping stone to a larger result rather than an independent statement, in and of itself. ...

• fundamental theorem of algebra
• fundamental theorem of arbitrage-free pricing
• fundamental theorem of arithmetic
• fundamental theorem of calculus
• fundamental lemma of calculus of variations
• fundamental theorem of curves
• 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

There are also a number of fundamental theorems not directly related to mathematics: In mathematics, the fundamental theorem of algebra states that every complex polynomial of degree n has exactly n roots (zeroes), counted with multiplicity. ... In mathematical finance, a risk-neutral measure is a probability measure in which todays fair (i. ... In mathematics, and in particular number theory, the fundamental theorem of arithmetic or unique factorization theorem is the statement that every positive integer greater than 1 is either a prime number or can be written as a product of prime numbers. ... The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverses of each other. ... Jump to: navigation, search The fundamental lemma of the calculus of variations states that if f is a function in C [a,b], and for every function h ∈ C2[a,b] with h(a) = h(b) = 0, then f(x) is identically zero in the open interval (a,b). ... In differential geometry, the fundamental theorem of curves states that any regular curve with non-zero curvature has its shape (and size) completely determined by its curvature and torsion. ... In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. ... In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions. ... In abstract algebra, for a number of algebraic structures, the fundamental theorem on homomorphisms relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism. ... In mathematics, the fundamental theorem of linear algebra makes several statements regarding vector spaces. ... In mathematics, the fundamental theorem of projective geometry states that if Pn is a projective space and F and F′ are frames of Pn, then there exists a unique projective transformation sending F to F′. In case n = 1 this comes down to saying that given two ordered triples of... In Riemannian geometry, the fundamental theorem of Riemannian geometry states that given a Riemannian manifold (or pseudo-Riemannian manifold) there is a unique torsion-free connection preserving the metric tensor. ... The fundamental theorem of vector analysis states that any vector field meeting certain conditions (of decaying towards infinity) can be resolved into irrotational and solenoidal component vector fields. ...

• Fisher's fundamental theorem of natural selection
• fundamental theorem of poker
• fundamental theorems of welfare economics