Cauchy-Schwarz Inequality
Fundamental inequality. Defines angle in inner product spaces.
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Similar Mathematical Theorem
Cayley-Hamilton Theorem
Matrix algebra fundamental result. Computing matrix powers.
Fundamental Theorem of Calculus
Connects differential and integral calculus. Enables calculation of areas and rates.
Hahn-Banach Theorem
Separates convex sets. Foundation of optimization.
Fundamental Theorem of Algebra
Guarantees polynomial equations solvable in complex numbers.
Bolzano-Weierstrass Theorem
Foundation of analysis. Compactness in real numbers.
Lagrange's Theorem
Fundamental group theory. Cosets and quotients.
Hilbert's Basis Theorem
Commutative algebra cornerstone. Ascending chain condition.
Bolzano's Theorem
Special case of intermediate value theorem. Root finding.
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Discover connections across different types of entities
Gauss's Law
Part of Maxwell's equations. Relates charge to electric field.
Noether's Theorem
Time symmetry gives energy conservation. Space symmetry gives momentum conservation.
CPT Theorem
Fundamental symmetry of nature. Antimatter and time reversal.
Snell's Law
Refraction law. n₁sin(θ₁) = n₂sin(θ₂). Explains lenses.
Wittgenstein on the limits of language
Wittgenstein on the limits of language
Einstein on the nature of reality
Einstein on the nature of reality
Schrödinger Equation
Fundamental equation of quantum mechanics. Predicts probability distributions.
Wien's Displacement Law
Why hot objects change color. λmax = b/T.