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.[1]
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 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.
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Fundamental lemmas
Fundamental theorems of mathematical topics
- 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
Non-mathematical fundamental theorems
There are also a number of "fundamental theorems" (more aptly a series of rule of thumb) 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
See also
Notes
- ^ K. D. Joshi (2001). Calculus for Scientists and Engineers. CRC Press. pp. 367–8. http://books.google.ca/books?id=5SDcLHkelq4C. Retrieved 2009-03-01.
- ^ Thomas C. Hales (2003). A Statement of the Fundamental Lemma. http://arxiv.org/abs/math.RT/0312227. (This was written before Ngo Bao Chau's announcement of the proof.)
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