| Term | Definition |
|---|
| Thales | the first greek known to have used proof and strict logical reasoning to solve mathematical questions |
| Pythagoras | influential Greek philosopher and religious leader. He taught that numbers and ratios of numbers were the foundation or reality. He discovered many number patterns and the proof that the square root of two is not rational |
| Euclid | Organized Greek geometry into a mathematical system based on fundamental definitions, a few postulates and theorems that are logically deduced. This work, known as the Elements, had a profound influence on mathematics for thousands of years. |
| Archimedes | Discovered many fundamental properties of physics, such as the law of the lever; discovered a way to approximate pi as accurately as desired |
| Apollonius | Discovered the family of curves known as the conic sections. He analyzed their properties using Greek geometry (not, however, with modern algebra equations or graphing techniques) |
| Ptolemy | Invented a planetary system that was adopted as truth by the Christian church in Medieval Europe. In this system the Earth does not move and the planets, moon, stars and the sun revolve around the earth in circular paths with consstant motion. This was described in his book the Almagest. |
| Al-Khwarizmi | Wrote influential Arabic books on solving algebra problems and the Hindu- Arabic numeration system. |
| Viete | Introduced symbols into algebra |
| Descartes | Developed analytic geometry. He used a sophisticated symbolic algebra to show how algebra can be used to solve geometry problems and how algebra problems can be solved with geometry |
| Fermat | developed analytic geometry. He showed how a geometric curve, such as a conic section, could be drawn on a coordinate grid from an algebra equation. He also made important contributions to number theory, |
| Kepler | Used real astronomical data to show that the planets orbit the sun in elliptical paths at varying rates of speed |
| Newton | Co-inventor of the calculus. He proved Kepler's laws mathematically in the style of Euclid in his book the Principia |
| Leibniz | Co-inventor of the calculus. His methods and symbolism is used today. |
| Euler | A founding father to many branches of mathematics. He lived in the generation that followed Newton and Leibniz. Modern calculus textbooks derive from his works on calculus. He is also responsible for many modern symbols, such as f(x), e, i, and PIE. |
| Gauss | Discovered non-Euclidean geometry. He was a pioneer in many ares of modern mathematics. |
| Cantor | Invented the theory of infinite sets. He proved that the counting number and the real numbers have a different cardinality |
| von Neumann | Designed the fundamental structure of modern computer design, known as the "." He also invented a branch of mathematics known as "game theory." |
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