List of theorems called fundamental

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In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus.[1] The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory.[2]

Likewise, 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.

Fundamental theorems of mathematical topics[edit]

Carl Friedrich Gauss referred to the law of quadratic reciprocity as the "fundamental theorem" of quadratic residues.[3]

Applied or informally stated "fundamental theorems"[edit]

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

Fundamental lemmata[edit]

See also[edit]


  1. ^ Apostol, Tom M. (1967), Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (2nd ed.), New York: John Wiley & Sons, ISBN 978-0-471-00005-1
  2. ^ Hardy, G. H.; Wright, E. M. (2008) [1938]. An Introduction to the Theory of Numbers. Revised by D. R. Heath-Brown and J. H. Silverman. Foreword by Andrew Wiles. (6th ed.). Oxford: Oxford University Press. ISBN 978-0-19-921986-5. MR 2445243. Zbl 1159.11001.
  3. ^ Weintraub, Steven H. (2011). "On Legendre's Work on the Law of Quadratic Reciprocity". The American Mathematical Monthly. 118 (3): 210. doi:10.4169/amer.math.monthly.118.03.210.

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