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Theorem	Mathematician	Field	Year	Difficulty	Status
Pythagorean Theorem In a right triangle, a² + b² = c²	Pythagoras		500 BC	Level 2
Fundamental Theorem of Calculus Links differentiation and integration	Isaac Newton & Gottfried Leibniz		1666	Level 7
Fermat's Last Theorem No three positive integers satisfy aⁿ + bⁿ = cⁿ for n > 2	Andrew Wiles		1995	Level 10
Gödel's Incompleteness Theorems Any consistent formal system has unprovable truths	Kurt Gödel		1931	Level 9
Euler's Identity e^(iπ) + 1 = 0	Leonhard Euler		1748	Level 6
Central Limit Theorem Sum of random variables approaches normal distribution	Pierre-Simon Laplace		1810	Level 6
Riemann Hypothesis All non-trivial zeros of ζ(s) have real part 1/2	Bernhard Riemann		1859	Level 10
Cauchy's Integral Theorem Integral of holomorphic function over closed curve is zero	Augustin-Louis Cauchy		1825	Level 7
Banach Fixed-Point Theorem Contraction mappings have unique fixed points	Stefan Banach		1922	Level 7
Nash Equilibrium Theorem Every finite game has a mixed strategy equilibrium	John Nash		1950	Level 6

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