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