Gabriel Cramer Biography

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World of Mathematics on Gabriel Cramer

Gabriel Cramer labored in the shadow of his more well-known mathematical contemporaries. Cramer added to mathematical knowledge in the areas of analysis, determinants, and geometry. Both Cramer's ruleand Cramer's paradox, discussed below, were not completely new ideas, but Cramer contributed significantly to both. Cramer also introduced the idea of utility to mathematics. Some of Cramer's most important work concerned the history of mathematics, as Cramer often served as the editor of other mathematicians' writings.

Cramer was born July 31, 1704, in Geneva, Switzerland, to physician Jean Isaac Cramer and his wife, Anne Mallet. Educated in Geneva, Cramer had two brothers. One, Jean-Antoine, also became a doctor; the other, Jean, was a law professor. All three brothers took an interest in local government and its inner workings. Cramer was a lifelong bachelor.

At the age of 18, Cramer defended his thesis with a topic about sound. At age 20, he was appointed co-chair of mathematics at the Académie de la Rive, and led the geometry and mechanics classes. His co-chair was Giovanni Ludovico Calandrini, a friend who taught algebra and astronomy. They also split the salary designated for one chair. As professors, Cramer and Calandrini broke with tradition and allowed recitations in French instead of the traditional Latin, so that students without a Latin background could participate.

The pair were encouraged to travel to enhance their scholarship. Cramer went to Basle for five months in 1727, where he met and befriended, among others, Johann Bernoulli. Cramer continued to travel until 1729, visiting London, Leiden, and Paris, before returning to Geneva. In 1734, Cramer became full chair of the department when Calandrini was appointed to a philosophy professorship. In the same year, Cramer's activity in local government was marked by his service on the Conseil des Deux-Cents.

Cramer's sense of community extended to his mathematical colleagues. He edited the collected works of fellow mathematician Johann Bernoulli in four volumes, which were published in 1742. Cramer's other editorial projects included the works of Johann's brother, Jakob Bernoulli, and Christian Wolff. His accomplishments as a mathematics editor were vital for the support and circulation of mathematical knowledge, and he was one of the first scholars of note to contribute to mathematics in this manner.

Cramer's most important mathematical work was published in 1750, the same year he was appointed professor of philosophy at Académie de la Rive when Caladrini left to work for the Swiss government. Within the four volumes of Introduction à l'analyse des lignes courbes algebriques, Cramer delineated what came to be known as Cramer's rule, which provided a mechanism for linear equation solutions. Although deteminants were discovered by Gottfried Wilhelm Leibniz in 1693, it is Cramer who brought determinants and their uses to wide spread attention. Also in this text is Cramer's discussion of curve analysis which led to their rediscovery, which led to other mathematicians improving on his analysis.

Another important element featured in Cramer's text is what came to be known as Cramer's paradox. The paradox clarified a theorem first proposed by Colin Maclaurin, who pointed out that two separate cubic curves can meet at nine different points. Cramer added that a single cubic curve is itself defined by nine different points. Because Cramer's explanation for this phenomenon was lacking, other mathematicians fleshed it out. Cramer is also responsible for the concept of utility, which today links probability theory with mathematical economics.

In 1751, Cramer fell from a carriage and was confined to his bed for two months. His doctor recommended a rest in the south of France for his health because, in addition to the fall, he was overworked. Cramer died en route in Bagnoles, France, on January 4, 1752.