"One can invent mathematics without knowing much of its history. One can use mathematics without knowing much, if any, of its history. But one cannot have a mature appreciation of mathematics with a substantial knowledge of its history."
René Descartes was a French mathematician, scientist and philosopher. His work, La Géométrie, includes the application of algebra to geometry, from which we now have Cartesian geometry. He also made contributions to the theory of equations and invented the method of indices (as in x2) to express powers of numbers.
Descartes was educated at the Jesuit college of La Flèche in Anjou. He entered the college at the age of eight years, and studied there for eight years. Since his health was poor, he was granted permission to remain in bed until 11 o'clock in the morning, a custom he maintained until the year of his death.
He received a law degree from University of Poitiers in 1616, but he never practiced law. He was later enrolled in the military school at Breda. In 1618, he started studying mathematics and mechanics under the Dutch scientist Isaac Beeckman, and began to seek a unified science of nature. In 1619, he joined the Bavarian army.
From 1620 to 1628, Descartes traveled through Europe, spending time in Bohemia (1620), Hungary (1621), Germany, Holland and France (1622-23). By 1628 Descartes was tired of traveling and decided to settle down. He gave much thought to choosing a country suited to his nature and chose Holland. It was during his residence in Netherlands that he wrote his major works.
In 1649, Queen Christina of Sweden persuaded Descartes to go to Stockholm to give her instruction in philosophy. However, the Queen wanted to draw tangents at 5 a.m. and Descartes had to break the habit of his lifetime of getting up at 11 o'clock. After only a few months in the cold northern climate, walking to the palace very early every morning, he died of pneumonia.
Newton came from a family of modest yeoman farmers. In 1656, Newton's mother removed him from grammar school in Grantham where he showed little promise in academic work. She wanted him to become a farmer, however, he did not show any talent in farming. In the end, his family decided that he should be prepared for the university, and he entered Trinity College, Cambridge, in June 1661.
In Cambridge, Newton immersed himself in the new mechanical philosophy of Descartes, Gassendi, and Boyle; in the new algebra and analytical geometry of Vieta, Descartes, and Wallis; and in the mechanics and Copernican astronomy of Galileo.
A plague closed the University in the summer of 1665 and he had to return to Lincolnshire. There, in a period of less than two years, he made great achievements in the study of mathematics, optics, physics, and astronomy. During that period, he discovered the law of universal gravitation, began to develop calculus, and discovered that white light is composed of all the colors of the spectrum. These findings enabled him to make fundamental contributions to mathematics, astronomy, and theoretical and experimental physics.
Newton was professor at Cambridge from 1669 to 1701, succeeding his teacher Isaac Barrow as Lucasian professor of mathematics. In 1703 he was elected president of the Royal Society and was re-elected each year until his death. He was knighted in 1708 by Queen Anne, the first scientist to be so honoured for his work.
Gauss was was born in Brunswick, Germany, on April 30, 1777. By the age of three, he was able to perform long computations in his head; at 10, he studied algebra and analysis. While still a teenager, he made many fundamental discoveries. Among these were the method of "least squares" for handling statistical data, a proof that a 17-sided regular polygon can be constructed with a straight-edge and compass (this result was the first of its kind since discoveries by the Greeks 2000 years earlier), and his quadratic reciprocity theorem.
In 1801, Ceres (an asteroid) was observed by astronomers on three occasions before they lost track of it. Gauss used these three observations to calculate the orbit of Ceres. In carrying out this work, he showed that the variation inherent in experimentally derived data follows a bell-shaped curve, now called the Gaussian distribution. This achievement established Gauss's reputation as a scientific genius before he was 25 years old.