Mathematical Theorems
Hilbert's Basis Theorem
Commutative algebra cornerstone. Ascending chain condition.
Liouville's Theorem
Complex analysis fundamental. No non-constant bounded entire functions.
Jordan Curve Theorem
Intuitively obvious but hard to prove. Plane topology.
Cayley-Hamilton Theorem
Matrix algebra fundamental result. Computing matrix powers.
Lagrange's Theorem
Fundamental group theory. Cosets and quotients.
Taylor's Theorem
Approximates functions with polynomials. Remainder term.
Ratio Test
Tests series convergence. Power series radius.
Squeeze Theorem
Limit technique. Sandwich theorem.
Rolle's Theorem
Special mean value theorem. Critical points existence.
Bolzano's Theorem
Special case of intermediate value theorem. Root finding.
De Moivre's Theorem
Powers of complex numbers. Trigonometry and complex analysis.
Law of Large Numbers
Why statistics works. Foundation of probability theory.
Fundamental Theorem of Arithmetic
Every integer has unique prime factorization. Number theory cornerstone.
Spectral Theorem
Diagonalization of symmetric matrices. Quantum mechanics foundation.
Green's Theorem
2D version of Stokes theorem. Area calculation.
Noether's Theorem
Symmetry implies conservation. Deep physics-mathematics connection.
Stokes' Theorem
Generalizes fundamental theorem of calculus. Differential forms.
Divergence Theorem
Gauss theorem. Connects flux and divergence.
Intermediate Value Theorem
Intuitive but powerful. Guarantees roots exist.
Implicit Function Theorem
Guarantees existence of implicit functions. Crucial in multivariable calculus.
Mean Value Theorem
Connects function values to derivative. Fundamental in analysis.
Bayes' Theorem
Update beliefs with evidence. Machine learning core.