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:
“The same polarity of the male and female principle exists in nature; not only, as is obvious in animals and plants, but in the polarity of the two fundamental functions, that of receiving and penetrating. It is the polarity of earth and rain, of the river and the ocean, of night and day, of darkness and light, of matter and spirit.”
—Erich Fromm (1900–1980)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)