Riemann–Roch theorem
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The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. Wikipedia
Consequences: Clifford's theorem on special divisors; Riemann–Hurwitz formula
Field: Algebraic geometry and complex analysis
First proof by: Gustav Roch
First proof in: 1865