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Scipione dal Ferro develops a method for solving depressed cubic equations (cubic equations without an x2 term), but does not publish.
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Jyeshtadeva, a Kerala school mathematician, writes the “Yuktibhasa”, the world's first calculus text, which gives detailed derivations of many calculus theorems and formulae.
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Johannes Kepler discovers two of the Kepler-Poinsot polyhedra.
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Isaac Newton invents an algorithm for the computation of functional roots.
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Edmund Halley prepares the first mortality tables statistically relating death rate to age.
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John Machin develops a quickly converging inverse-tangent series for pie and computes pie to 100 decimal places.
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Abraham de Moivre introduces the normal distribution to approximate the binomial distribution in probability
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Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations.
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Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes.
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Joseph Louis Lagrange discovers the divergence theorem.
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Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms
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Georg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points.
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Josip Plemelj solves the Riemann problem about the existence of a differential equation with a given monodromic group.
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Kurt Gödel proves his incompleteness theorem which shows that every axiomatic system for mathematics is either incomplete or inconsistent,
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Nicholas Metropolis introduces the idea of thermodynamic simulated annealing algorithms
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Robert Langlands formulates the influential Langlands program of conjectures relating number theory and representation theory.
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Gerd Faltings proves the Mordell conjecture and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's Last Theorem.
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Neeraj Kayal of Ipresents an unconditional deterministic polynomial time algorithm to determine whether a given number is prime.