# Augustin-Louis Cauchy

# Augustin-Louis Cauchy

**1789-1857**

**French Mathematician**

During his impressive career Augustin-Louis Cauchy published 789 scientific papers, more than almost any other scientist in the history of science. These papers spanned all of the fields of mathematics of his day and helped to place calculus on a firm theoretical footing, expanding its utility in the study of physics and astronomy. Cauchy held very conservative political views, which caused him a great deal of trouble politically and professionally, but he adamantly refused to act in a way contrary to his beliefs at any time in his life.

Cauchy was born in Paris a month after the Bastille was stormed in the first of the French revolutions. His father, a government official, supported the King, which made life difficult for Cauchy and his family during his youth. Cauchy was educated at home, where Pierre Laplace (1749-1827) and Joseph Lagrange (1736-1813) were frequent visitors. Both were impressed by the young Cauchy's abilities and took an interest in his mathematical education. They encouraged his study of classical languages and mathematics at the Ecole Polytechnique, where he graduated in 1805. After graduation he was put to work as a military engineer for a time, until turning his attention entirely to mathematics in his mid-twenties.

Cauchy applied for several academic positions over the next few years without success. Finally, in 1815 he earned an appointment as an assistant professor of analysis at the Ecole Polytechnique and, at age 27, he became the youngest person to be elected to the Academie of Sciences, based on his work the theories of definite integrals and complex functions.

One of Cauchy's most significant accomplishments involved establishing conditions under which an infinite series will converge on a solution. He also established the first mathematically rigorous definition of an integral, a concept of fundamental importance to calculus. However, perhaps his greatest achievement was in developing the basic concepts of calculus in a rigorous manner. This placed calculus on a firm mathematical footing, helping to ensure its viability as a useful branch of mathematics. In particular, his theory of the continuity of functions and his work on limits not only helped to erect a logical framework for differential calculus, but are still taught today as essential for a full understanding of some of the most basic concepts of calculus.

During this period of his life, Cauchy earned a reputation for treating fellow mathematicians less than favorably. He refused to read some of the early work of Niels Abel (1802-1829), causing Abel to write that "Cauchy is mad and there is nothing that can be done about him, although, right now, he is the only one who knows how mathematics should be done." His treatment of Evariste Galois (1811-1832) was poor, too, and he was so harsh with Jean-Victor Poncelet (1788-1867) that Poncelet gave up trying to earn any regard or scientific respect at all.

Cauchy's religious and political beliefs kept him in trouble through much of his professional life. His refusal to take an oath of allegiance to the new French government in 1831 resulted in his losing his position at the university. He left France for several years, exiling himself to Italy where he continued to teach, at one point acting as tutor to the son of Charles X when the royal family was in exile, too. Cauchy eventually returned to France in 1838, regaining his position with the Academy. Later, after another change in government, the issue of loyalty oaths arose again. This time, however, Cauchy and Dominique Arago (1786-1853) were exempted from this requirement because of their importance to French science.

The final years of Cauchy's life were spent in more disputes, both scientific and personal. This led to some degree of bitterness and sadness that was apparent to his children and friends, if not to his colleagues and enemies. Cauchy died in 1857 at the age of 67, leaving behind a great legacy of work touching on almost every part of mathematics.

**P. ANDREW KARAM**

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**Augustin-Louis Cauchy**