List: Fundamental theorems in scinece

Clue: A fundamental theorem of complex analysis
Answer: Runges theorem
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Clue: A fundamental theorem of model theory
Answer: Ax Grothendieck theorem
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Clue: A fundamental theorem of group theory
Answer: Redeis theorem
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Clue: A fundamental theorem of vector calculus
Answer: Gauss theorem
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Clue: A fundamental theorem of algebraic curves
Answer: Belyis theorem
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Clue: A fundamental theorem of geometry
Answer: Thebaults theorem
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Clue: A fundamental theorem of operator theory
Answer: Banach Stone theorem
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Clue: A fundamental theorem of dynamical systems
Answer: Denjoy theorem
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Clue: A fundamental theorem of complex analysis
Answer: Picard theorem
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Clue: A fundamental theorem of triangle geometry
Answer: Eulers theorem in geometry
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Clue: A fundamental theorem of complex manifold
Answer: Branching theorem
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Clue: A fundamental theorem of number theory
Answer: Gross Zagier theorem
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