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
Incompleteness theorems), logic and set theory
Proved both axiom of choice and the continuum hypothesis are independent of other Zarmelo-Fraenkel axioms