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Heron of Alexandria references square roots of negative numbers.
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Diophantus uses symbols for unknown numbers and writes one of the earliest treatises on algebra, Arithmetica.
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Jaina mathematicians describe a theory of infinity, logarithms, and square roots of large numbers with an accuracy of 11 decimal places.
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Zu Chongzhi computes Pi to seven decimal places.
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Aryabhata defines the concepts of sine and cosine and includes tables for sine and cosine from 0 to 90 degrees.
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Hidu mathematicians give zero a numberical representation in the Indian numeral system.
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Virasena gives rules for Fibonacci Sequence.
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Muslim mathematicians discover the Law of Sines, though it is unclear who actually discovered it.
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Indian numberals are modified by Arab mathematicians to form universal number system.
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Bhaskara Acharya conceives differential calculus and developes Rolle's Theorem.
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Liber Abaci (Book of the Abacus) is written by Leonardo Fibonacci demostrating the use of the Hindu-Arabbic numerals.
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Ludolf van Ceulen computes pi using inscribed and circumscribes polygons. His computation was accurate to 20 decimal places.
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John Napier writes a book explaining Napierian logarithms.
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Both Rene Decartes and Pierre de Fermat claim to independently discover analytic geometry.
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Rene Decartes uses imaginary numbers.
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Blaise Pascal and Pierre de Fermat create the theory of probability.
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Issac Newton works on the Fundemental Theorem of Calculus and developes his discovery of infintesimal calculus.
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Gottfried Leibniz developes infinitesimal calculus about the same time as Newton.
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John Machin calculate pi to 100 digits using a quickly converging inverse-tangent series.
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Brook Tylor developes Taylor series.
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Abraham de Moivre connects trigonometric functions and complex numbers with de Moivre's Formula.
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Abraham de Moivre introduces an approximation of the binomial distribution using the normal distribution.
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Euler solve the Seven Bridges of Konigsber pioneering graph theory.
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Thomas Bayes proves Bayes' Theorem for use in probability.
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Johann Heinrich Lambert proves that pi is an irrational number.
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Carl Friedrich Gauss proves the Fundemental Theorem of Algebra stating that every polynomial has a solution in complex numbers.
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Adrien-Marie Legendre introduces the method of least squares to fit a curve to data.
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August Ferdinand Mobius invents the Mobius strip and introduces topology.
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Bernhard Riemann formulates the Riemann hypothesis having to do with the distribution of prime numbers.
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Felix Klein invents the Klein bottle expanding the field of topology in mathematics.
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John von Neumann computes pi to 2,037 places using the computer ENIAC.
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Lotfi Asker Zadeh, an Iranian mathematician, founded fuzzy set theory and later Fuzzy Mathematics.
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Al-Khwarizmi, a Persian mathematician, writes Al-Jabra. Later this would translate to Algebra. The book includes methods for solving linear and quadratic equations using algorithms (which is also named after him.)
