The fundamental theorem of a field of mathematics is the theorem considered central to that field. The naming of such a theorem is not necessarily based on how often it is used or the difficulty of its proofs.
For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus, which are two distinct branches that were not obviously related.
The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory.
The mathematical literature sometimes refers to the fundamental lemma of a field. The term 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. The fundamental lemma of a field is often, but not always, the same as the fundamental theorem of that field.
Read more about Fundamental Theorem: Fundamental Lemmata, Fundamental Theorems of Mathematical Topics, Non-mathematical Fundamental Theorems
Famous quotes containing the words fundamental and/or theorem:
“Each [side in this war] looked for an easier triumph, and a result less fundamental and astounding. Both read the same Bible, and pray to the same God; and each invokes His aid against the other. It may seem strange that any men should dare to ask a just God’s assistance in wringing their bread from the sweat of other men’s faces; but let us judge not that we be not judged.”
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“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
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