thought of the universe rationally

Euclid's Elements discusses the definitions, axioms, and postulates of Euclidean Geometry

developed what is now modern day calculus

trigonometry

continued on with Hipparchus's work in trigonometry

Hindus made contributions to arithmetic and algebra. First to recognize negative numbers.

The Roman emperor declared Christianity to be the official religion.

Used Ptolemy's work on astronomy to create a new theory.

Viete was the first to use variables in place of numbers in equations.

Invented logarithms.

Through building a telescope, Galileo was able to see the uneven surface of the moon, the rings around Saturn, four of the moons on Jupiter, and that the Milky Way was made up of thousands of stars. He was a supporter of Copernicus and Kepler's theory because of the observations he made. He believed nature to be made by God mathematically.

Studied Ptolemy and Copernicus's work and developed three laws of the motion of planets.

English Philosopher who followed Descartes mechanistic theory.

Built on the Greek doctrine of primary and secondary qualities. He devised the law of inertia, which is now known as Newton's first law of motion.

Changed the course of science by using mathematics instead of physical hypotheses. One of the biggest contributors to calculus.

His work, Essays de Theodice, outlined his belief that God created the world mathematically. One of the biggest contributors to calculus, specifically, he developed infinitesimal calculus.

This book shows the use of mathematics in proving natural phenomena.

Huygens described the light to be particles of ether creating a motion of light as they move.

Known for his work in geometry, calculus, and number theory. He also was the first to use symbols for various things, including functions.

Kant believed in intuitionism. He formed the thesis of intuitionism stating that truth comes from the mind.

Established the theory of differential equations.

Diderot was one of the first to say that the truths mathematics was based on for so long were in fact not truths.

Developed the concept of the Fourier series.

Proved the Fundamental Theorem of Algebra. Work on the foundation of number theory.

Recognized for building the logic of calculus on the concept of limits. Cauchy developed the concepts of function, limit, continuity, derivative, and integral upon solid definitions.

Published works on definite integrals and the theory of numbers. He used limits and continuity to explain calculus. He developed the theory of functions for complex variables.

Used his principle of the permanence of equivalent forms as justification to using operations with complex numbers.

Lobachevsky published his work on non-Euclidean geometry which stated his thoughts on the foundations of geometry.

Book covering the theory of numbers.

Published a paper on absolute geometry. This is his version of non-Euclidean geometry which he believed was not self-contradictory.

Introduced matrices, a square or rectangular array of numbers. Matrices did not follow the commutative property of multiplication. It is also possible to multiply two matrices and get a product of zero even if neither matrice is zero.

Weierstrass was the first to rigorize irrational numbers by deriving their properties and providing clear definitions of the properties similar to rational numbers.

Created the new numbers, called quaternions. These numbers did not hold to the commutative property of multiplication.

Proposed an algebra of logic. Used reasoning of algebraic operations in various mathematical fields.

Cantor founded set theory. He also introduced transfinite numbers. He showed that even with infinite sets, they were still sets of different sizes.

Formalized material implication for conditional statements. Led the way to the axiomatization of logic. He was a leader in the school of logicism.

A mathematical physicist who made advances in geometry and the differential equations.

Whitehead was a leader in the school of logicsim.

Double elliptic geometry applies to the surface of a sphere where the lines are considered to be the great circles of the sphere. Hence, this non-Euclidean geometry was considered consistent based on the fact that Euclidean geometry was consistent.

Russell was a leader in the school of logicism.

Leader of the school of intuitionism. Believed mathematics was not independent of the human mind. Saw mathematics as the process of mental constructing.

While many mathematicians believed they had completely rigorized mathematics, Hilbert presented a list of 23 problems needing attention at the Congress of 1900. He developed the formalist school of thought and treated mathematics as symbols that can be manipulated

Founder of symbolic logic

Theorems of Incompleteness explained that an infinite number of axioms created an inconsistent system of mathematics.

Sought the maximization of set theory which became the foundation of the set-theoretic school of thought.

Written by Whitehead and Russell while attempting to place mathematics on the foundation of logic.