Pythagoreans offer mathematical plan of nature

Discovers light travels with finite velocity

Along with Leuccipus, explicit in affirming doctrine of atomism

Along with Democritus, explicit in affirming the doctrine of atomism

Took over some Pythagorean doctrines. Founded the Academy in Athens. Influential teacher. Insisted on rigorous proof and logical methods

Criticized Plato. Believed in material things as the primary source of reality. Development of logic and deductive reasoning

Trained students in Alexandria and pulled together geometrical ideas

Added several works to Apollonius' Conic Sections

made numerous calculations of distances between significant portions of the earth known to Greeks

Carried on Euclid's study of the parabola, ellipse, and hyperbola

Found formula for finding the area of a triangle using its side lengths and method for computing a square root

Analyzed complex algebraic problems to find rational solutions to equations with unknowns.

Discovered basic mathematical rules for dealing with zero, negative numbers, negative roots of quadratic equations, and found solutions for quadratic equations

Leading mathematician of the 12th century. Introduced some preliminary concepts of calculus

Published book on arithmetic and geometry and introduced standard symbols.

Invented natural logarithms.

Developed Cartesian coordinates and analytic geometry. Also gets credit for the use of exponents.

Extended knowledge of number theory and contributed to probability theory

Pioneer of probability theory. Pascal's triangle.

Development of differentiation and integration. Laid ground work for almost all of classical mechanics, infinite power series, and generalized binomial theorem

His calculus notation is still used. Created practical calculating machine using binary system. Used matrix to solve linear equations

Made important contributions in all fields and discovered links between fields. Developed new methods and proved many theorems

Fundamental Theorem of Algebra, least squares approximation method, Gauss distribution, Gauss function, non-Euclidean geometry, Gaussian curve

(and Bolyai) Developed theory of hyperbolic geometry

Non-Euclidean elliptic geometry, Riemann geometry

Set theory

Incompleteness theorems), logic and set theory

Proved both axiom of choice and the continuum hypothesis are independent of other Zarmelo-Fraenkel axioms