## Mathematician of the week: Johann Lambert

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Johann Lambert was born on August 26, 1728. (His father, Lukas Lambert, was a tailor, and was not involved in the discovery of a primality test for Mersenne numbers.)

By the time he was a teenager, Lambert found himself working full-time for his father, while pursuing his academic studies at night. Over the ensuing decade, Lambert held a number of jobs while teaching himself mathematics and science. He first attracted attention on the academic stage with an article on heat, published in 1755. A mere three years later Lambert published a book on the passage of light through various media.

Lambert struggled throughout his life to find academic employment, but in spite of that he was quite prolific, publishing over 150 articles and books by the time of his death at the age of 49.

He had two particularly significant mathematical contributions:

• His Theorie der Parallellinien (1766) was a study of the consequences of the negation of the parallel postulate, including the correlation between the sum of the angles of a triangle and its area in a non-euclidean geometry.
• In 1768, Lambert gave the first rigorous proof of the irrationality of π. Specifically, he showed that if x is a nonzero rational number, then both $e^x$ and $\tan x$ must be irrational, using the continued fraction representations of those two functions.