## Gabriel Cramer

## Gabriel Cramer

# Gabriel Cramer

**1704-1752**

**Swiss Mathematician**

The name Gabriel Cramer is associated with Cramer's rule and Cramer's paradox, as well as with the introduction of the concept of utility to mathematics. Yet perhaps Cramer's greatest contributions to learning emerged from his support of other talented contemporaries, specifically in his work as editor of their writings.

Born in Geneva on July 31, 1704, Cramer was the son of Jean, a physician, and Anne Mallet Cramer. He came from a family of three brothers, one of whom became a doctor and the other a professor of law. By the age of 18, Cramer had earned his doctorate with a dissertation on the qualities of sound, and two years later was appointed co-chair of mathematics at the Académie de la Rive. He shared both the position and the salary with Giovanni Ludovico Calandrini, and the two men broke new ground by allowing students who knew no Latin to recite in French instead.

Encouraged by the Académie to travel as a means of expanding his knowledge, in 1727 Cramer spent five months in Basel, where he became acquainted with Johann Bernoulli (1667-1748). Over the two years that followed, he visited London, Leiden, and Paris. Five years after his return to Geneva in 1729, Cramer was appointed full chair of the department after Calandrini received an appointment to a philosophy professorship.

Along with his brothers, Cramer had long taken part in local politics, and he likewise displayed a sense of community spirit where the world of mathematics was concerned. Among the mathematicians and thinkers whose work he edited were Johann and his brother Jakob Bernoulli (1654-1705), as well as the German philosopher and mathematician Christian Wolff (1679-1754). Thus he helped spread these men's ideas, and contributed greatly to their success.

In 1750, Cramer was appointed professor of philosophy at the Académie (Calandrini had left his post to serve the Swiss government), and published the four-volume *Introduction à l'analyse des lignes courbes algébriques.* The work contained Cramer's rule, which governed the solutions of linear equations, and Cramer's paradox, which clarified a proposition first put forth by Colin Maclaurin (1698-1746) regarding points and cubic curves. In addition, Cramer introduced the concept of utility, a key principle today linking probability theory and mathematical economics.

A year after publishing his most important mathematical work, Cramer suffered a fall from a carriage. The scholar had long been overworked and suffering from fatigue, so his doctor recommended that he rest in the south of France. On January 4, 1952, however, Cramer died on his way to the town of Bagnoles.

**JUDSON KNIGHT**