fundamental theorem

fundamental theorem (plural fundamental theorems)

1. (chiefly mathematics) A theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field.
   • 1994, Joseph E. Stiglitz, Whither Socialism?, The MIT Press, page 27,

     In this and the next chapter I return to the fundamental theorems of welfare economics. In this chapter I argue that the first fundamental theorem of welfare economics—asserting the efficiency of competitive economics—is fundamentally flawed.

   • 2010, Vasily E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, page 247,

     The first fundamental theorem of calculus states that the differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is obtained […] .

   • 2012, Joseph L. Taylor, Foundations of Analysis, American Mathematical Society, page 114,

     There are two fundamental theorems of calculus. Both relate differentiation to integration. In most calculus courses, the Second Fundamental Theorem is usually proved first and then used to prove the First Fundamental Theorem. Unfortunately, this results in a First Fundamental Theorem that is weaker than it could be.

In usages outside mathematics proper, some fundamental theorems may still be expressed mathematically and even "proven" in the context of an accepted mathematical model.

• fundamental lemma