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Physical Theorem

Conservation of Momentum

Momentum before equals momentum after. No external forces.

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Discover connections across different types of entities

Mathematical Theorem

Noether's Theorem

Symmetry implies conservation. Deep physics-mathematics connection.

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Visual Art

The Decisive Moment

Cartier-Bresson's photograph captures a man leaping over a puddle in perfect geometric composition. The work …

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Mathematical Theorem

Divergence Theorem

Gauss theorem. Connects flux and divergence.

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Mathematical Theorem

Spectral Theorem

Diagonalization of symmetric matrices. Quantum mechanics foundation.

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Quote

On the gap between intention and outcome

On the gap between intention and outcome

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Mathematical Theorem

Intermediate Value Theorem

Intuitive but powerful. Guarantees roots exist.

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Mathematical Theorem

Cayley-Hamilton Theorem

Matrix algebra fundamental result. Computing matrix powers.

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Philosophical Concept

Determinism

Philosophical view that all events are determined by prior causes. Hard determinism denies free will—every …

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Mathematical Theorem

Euler's Identity

Most beautiful equation. Connects five fundamental constants.

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Philosophical Concept

Dualism

Metaphysical view that mind and body are distinct substances. Cartesian substance dualism: mind (res cogitans) …

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