Liouville's Theorem
Complex analysis fundamental. No non-constant bounded entire functions.
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De Moivre's Theorem
Powers of complex numbers. Trigonometry and complex analysis.
Lagrange's Theorem
Fundamental group theory. Cosets and quotients.
Fundamental Theorem of Algebra
Guarantees polynomial equations solvable in complex numbers.
Bolzano-Weierstrass Theorem
Foundation of analysis. Compactness in real numbers.
Brouwer Fixed Point Theorem
Every continuous function from ball to itself has fixed point.
Fundamental Theorem of Calculus
Connects differential and integral calculus. Enables calculation of areas and rates.
Divergence Theorem
Gauss theorem. Connects flux and divergence.
Implicit Function Theorem
Guarantees existence of implicit functions. Crucial in multivariable calculus.
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Discover connections across different types of entities
The Fold
Leibnizian-Deleuzian concept of infinite folding as nature's operation. Matter folds infinitely inward; soul unfolds infinitely …
CPT Theorem
Fundamental symmetry of nature. Antimatter and time reversal.
Schrödinger Equation
Fundamental equation of quantum mechanics. Predicts probability distributions.
Heisenberg Uncertainty Principle
Fundamental limit of measurement. Not about instruments but nature itself.
Noether's Theorem
Time symmetry gives energy conservation. Space symmetry gives momentum conservation.
Bernoulli's Principle
Explains airplane lift. Venturi effect. Energy conservation in fluids.
All's Well That Ends Well on complexity
All's Well That Ends Well on complexity
Third Law of Thermodynamics
Entropy approaches constant as temperature approaches absolute zero.