Mathematicians and the Events in the Development of Mathematics

Events

Pythorgreans - a mathematical plan of nature

585 BC - 500 BC

Plato

427 BC - 347 BC

thought of the universe rationally

Euclid

300 BC

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

Archimedes

287 BC - 212 BC

developed what is now modern day calculus

Hipparchus

125 BC

trigonometry

Menelaus of Alexandria

98 BC

continued on with Hipparchus's work in trigonometry

Hindus

200 - 1200

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

Constantine the Great

315

The Roman emperor declared Christianity to be the official religion.

Nicolas Copernicus

1473 - 1543

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

Francois Viete

1540 - 1603

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

John Napier

1550 - 1617

Invented logarithms.

Galileo Galilei

1564 - 1642

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.

Johannes Kepler

1571 - 1630

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

Thomas Hobbs

1588 - 1679

English Philosopher who followed Descartes mechanistic theory.

Rene Descartes

1596 - 1650

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.

Sir Isaac Newton

1642 - 1727

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

Gottfried Leibniz

1646 - 1716

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.

Newton's Mathematical Principles of Natural Philosophy

1687

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

Huygens' Treatise on Light

1690

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

Leonhard Euler

1707 - 1783

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

Immanuel Kant

1724 - 1804

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

Joseph -Louis Lagrange

1736 - 1813

Established the theory of differential equations.

Diderot's Thought on the Interpretation of Nature

1753

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

Joseph Fourier

1768 - 1830

Developed the concept of the Fourier series.

Karl Gauss

1777 - 1825

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

Augustin-Louis Cauchy

1789 - 1857

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.

Augustin-Louis Cauchy

1789 - 1857

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.

George Peacock

1791 - 1858

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

Nikolai Lobachevsky

1793 - 1856

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

Karl Gauss's Arithmetical Dissertations

1801

Book covering the theory of numbers.

Johann Bolyai

1802 - 1860

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

Gauss developed non-Euclidean geometry

1813

Arthur Cayley

1821 - 1895

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

Approx. 1840

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

William R. Hamilton

1843

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

George Boole

1844

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

Georg Cantor

1845 - 1918

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

Gottlob Frege

1848 - 1925

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

Henri Poincare

1854 - 1912

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

Alfred North Whitehead

1861 - 1947

Whitehead was a leader in the school of logicsim.

Eugenio Beltrami

1868

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.

Bertrand Russell

1872 - 1970

Russell was a leader in the school of logicism.

Luitzen E.J. Brouwer

1881 d.C

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

David Hilbert

Approx. 1900

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

Leibniz's earlier work on logic known

1901

Founder of symbolic logic

Kurt Godel

1906 - 1978

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

Ernst Zermelo

1908

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

Principia Mathematica

Approx. 1910

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