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Physical Theorem

Third Law of Thermodynamics

Entropy approaches constant as temperature approaches absolute zero.

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Discover connections across different types of entities

Mathematical Theorem

Law of Large Numbers

Why statistics works. Foundation of probability theory.

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Mathematical Theorem

Banach-Tarski Paradox

Uses axiom of choice. Demonstrates measure theory limits.

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Mathematical Theorem

Spectral Theorem

Diagonalization of symmetric matrices. Quantum mechanics foundation.

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Mathematical Theorem

Divergence Theorem

Gauss theorem. Connects flux and divergence.

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Mathematical Theorem

Noether's Theorem

Symmetry implies conservation. Deep physics-mathematics connection.

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Mathematical Theorem

Euler's Identity

Most beautiful equation. Connects five fundamental constants.

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Mathematical Theorem

Rolle's Theorem

Special mean value theorem. Critical points existence.

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Mathematical Theorem

Central Limit Theorem

Why normal distribution ubiquitous. Statistics foundation.

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Mathematical Theorem

Brouwer Fixed Point Theorem

Every continuous function from ball to itself has fixed point.

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Mathematical Theorem

De Moivre's Theorem

Powers of complex numbers. Trigonometry and complex analysis.

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