# Johann Heinrich Lambert

# Johann Heinrich Lambert

**1728-1777**

**Swiss-German Mathematician**

Overcoming enormous social barriers, Johann Heinrich Lambert entered the ranks of Europe's foremost mathematicians. He did so without becoming part of the Continental academic establishment and, partly for that reason, much of his most advanced work was lost for many years, including his studies of what came to be known as non-Euclidean geometry. Nonetheless, he contributed to the knowledge of pi and the theory of errors.

Born on August 25, 1728, in Mulhouse, an independent town allied with Switzerland, Lambert was the son of Lukas (a tailor) and Elisabeth Lambert. Because of the family's poverty, he had to leave school at age 12 to help his father, but, during the years that followed, he progressed to more professional positions. Thus, by 1745, when he was 17, Lambert was working as secretary to the editor of a newspaper in Basel, Switzerland. Two years later, when his father died, he obtained employment with a wealthy family as tutor to their children.

During the period from 1756 to 1758, Lambert and his young charges traveled around the continent, giving him an opportunity to advance his knowledge of mathematics. He was elected a corresponding member of the Learned Society at Göttingen, and, although he was offered a position at St. Petersburg, where he would have joined some of the leading intellectual figures of the day, he chose to remain in western Europe. By 1761, he had been proposed for membership in the Prussian Academy and, four years later, began receiving a full salary from the academy.

Lambert's pursuits with the Prussian Academy were varied. Influenced by the work of Gottfried Leibniz (1646-1716), he took part in an ultimately fruitless attempt to realize the philosopher-mathematician's dream of a universal language for reasoning. More successful were Lambert's efforts on a much older problem, that of "squaring the circle," that is, creating a square of the exact same size as a given circle. To do so requires an understanding of the number pi, and Lambert's achievement was to prove that π is not a rational number; in other words, π cannot be expressed as the ratio of two whole numbers. Also during this period of Lambert's career, when he produced some 150 papers under the aegis of the Prussian Academy, he worked on an early version of non-Euclidean geometry.

Lambert's work on non-Euclidean geometry was well ahead of its time, as was his attempt at a general theory of errors. While measuring light, he developed a method for calculating the probability distribution of errors, a method that would be used by statisticians a century later. Anticipating various aspects of chaos mathematics, he analyzed the weather, treating it as the outcome of an apparently limitless number of unknown causes. The mathematician died in Berlin on September 25, 1777.

**JUDSON KNIGHT**

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