There are several important theorems often described as fundamental within their respective sub-fields:
- Fundamental theorem of calculus, linking integration and differentiation
- Fundamental theorem of algebra, for roots of polynomial functions
- Gradient theorem, called the fundamental theorem for line integrals
- Fundamental theorem of contour integrals, the complex analysis equivalent
- Helmholtz’s decomposition theorem, called the fundamental theorem of vector calculus
- Rank-nullity theorem, sometimes called the fundamental theorem of linear algebra