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 theorem of algebra
• fundamental theorem of arbitrage-free pricing
• fundamental theorem of arithmetic
• fundamental theorem of (the) calculus
• fundamental theorem (or lemma) of (the) calculus of variations
• fundamental theorem of curves
• fundamental theorem of finitely generated abelian groups
• 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 Galois theory

There are also a number of fundamental theorems not directly related to mathematics:

• Fisher's fundamental theorem of natural selection
• fundamental theorem of poker