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No great discovery was ever made without a bold guess.
-Isaac Newton

On this page you will find a list of the 10 most famous and important mathematicians who have changed the course of human history. The most influential mathematicians are listed here, along with a short biography for each one.

1. Sir Isaac Newton
He was not only a brilliant mathematician, but also an astronomer and a physicist. Born in England on Christmas Day 1642, he invented calculus when he was in his early 20s, at about the same time as Gottfried Leibniz also did, independently.

He proved that white light could be decomposed in a mixture of different colors (the colors of the rainbow), built the first reflecting telescope, discovered the binomial theorem, was the first to use polar coordinates, and realized that the force that causes an apple to fall to the ground is also responsible for the movement of planets and stars.

He said that many of the discoveries he made in physics were the result of random playing rather than directed experimentation.

Newton, like some other great scientific geniuses was a bit strange. He had not the slightest interest in sex, never married, and almost never laughed. He also suffered a massive mental breakdown, and was probably manic depressive throughout his life.

2. Johann Carl Friedrich Gauss
He worked in a wide variety of domains that include algebra, probability and statistics, analysis, number theory, differential geometry, geodesy, astronomy, magnetism, and optics.

The Duke of Brunswick noticed his genius when he was very young and paid for his education. A notebook belonging to Gauss, written in Latin when he was only 15, was found in 1989. It shows that he had obtained remarkable results pertaining to non-Euclidian geometry, and to the prime number theorem.

The papers that he published include some on magnetism, optics, differential equations, astronomy, and the theory of errors.

3. Euclid
(365-300 B.C.)
He is the author of the earliest substantial Greek mathematical treatise to have survived, The Elements. Because of this, it makes him the leading mathematics teacher of all time. This treatise has been used to teach geometry for some 2500 years, and to help students of mathematics to think systematically.

He also wrote works on astronomy, optics, music, and geometry, many of which have been lost forever.

4. Leonhard Euler
He is known as the most prolific mathematician in history. Born in Switzerland, he became completely blind, but still made major contributions to modern analytic geometry, trigonometry, calculus, and number theory.

During his life he wrote over 8000 books and papers, on every aspect of physics and mathematics. Some of these papers were still being published for the first time, more than 200 years after his death. He studied infinite series and differential equations, and created the calculus of variations.

His notations such as e and p (pi) are still used today. He studied the motion of rigid bodies in 3 dimensions, the construction and control of ships, and celestial mechanics.

Euler's collected works have been printed bit by bit since 1910, and will eventually occupy more than 75 books.

5. David Hilbert
This German mathematician and philosopher, is considered by many to be the foremost mathematician of the 20th century.

He contributed to the theory of algebra, number fields, integral equations, functional analysis, and applied mathematics. His work in geometry is second after Euclid's.

His famous 23 Paris problems, formulated in 1900, still raise important mathematical questions today and offer renewed challenges to mathematicians. Many of these 23 problems have been solved, some just recently, and some still remain unsolved after over a 100 years.

6. Jules Henri Poincare
He was a French mathematician, mathematical physicist, astronomer and philosopher. He invented algebraic topology and the theory of analytic functions of several complex functions. He also studied optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, and the theory of relativity and cosmology.

He codiscovered, with Albert Einstein and Hendrik Lorentz, of the special theory of relativity.

7. Georg Friedrich Bernhard Riemann
Born in Germany, he had an important influence on the study of geometry in space and the modern theory of relativity. His contribution to the field of integrals is important, and he defined what are now called Riemann integrals.

Publications in 1851 and in 1857, introduced the concept of "Riemann surface" to deal with multivalued algebraic functions and it became a major idea in the development of analysis.

A famous lecture he gave  in 1854 in the presence of Gauss ("On the hypotheses that underlie Geometry") first introduced the concept of a manifold (an n-dimensional curved space).  

8. Evariste Galois
Became famous for his contributions to group theory. The solutions he came up with were often so innovative that his university teachers failed to appreciate them. He was also able to perform many calculations in his head that he would not bother to outline in his arguments.

He had quite a temper and was eventually taunted into a duel, that he accepted knowing he would die. He spent his last night, writing his mathematical ideas and discoveries in as complete a form as he could.

The next day he was shot in the stomach and died. No until 1846 had group theory progressed sufficiently for his discoveries to be appreciated. His legacy has had a great impact on 20th century mathematics.

9. Rene Descartes
French mathematician and philosopher who wrote one of the most influential geometry books in history, "La geometrie". He made important contributions in astronomy, including a theory of vortices, and more especially in mathematics, where he reformed algebraic notation and helped found coordinate geometry.

The coordinate system of reference is often referred to as the Cartesian plane in his honor. 

10. Blaise Pascal
He founded probability theory at the same time, but independtly, as Pierre de Fermat. Pascal also invented the first calculating machine, he studied conic sections, and produced important theorems in projective geometry.

He worked out the first 23 propositions of Euclid by the time he was 11 years old. At 16, he published essays on conics that Descartes refused to believe were the work of a teenager. In 1654, he decided that religion was more important, so he joined his sister in her convent and gave up mathematics and social life.

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