# Augustin Louis Cauchy

## Early Developer of the Calculus

His father moved the family to Arcueil where he provided for them as best he could and wrote textbooks to educate his children. Cauchy’s early malnutrition affected his health for the rest of his life.

One of the family’s neighbors in Arcueil was the well known mathematician Pierre Laplace; he met with young Cauchy and encouraged him in mathematics. When Cauchy was 11, his father was appointed Secretary of the Senate and it was in this office that Cauchy met another famous mathematician, Joseph Lagrange. Lagrange, who also recognized Cauchy’s mathematical talents, advised Cauchy’s father on the boy’s education, suggesting a well rounded course of study. Cauchy was very successful in school, winning prizes in Latin and Greek, and at 16 entered the École Polytechnique in Paris. Here his principled and obstinate character was revealed in his public observance of Catholicism when quiet religious observance might have been an easier path to follow. Following two years of training in engineering he was given a commission in Napoleon’s army and spent the next three years in Cherbourg as an engineer. In addition to his military work, he continued to study and teach mathematics.

Cauchy returned to Paris in 1813 and began to write at a fantastic pace, producing papers on several mathematical topics including the relationship between the number of sides, edges, and vertices of a polyhedron, and a solution to a problem on polygonal numbers posed by PIERRE DE FERMAT. This prolific writing continued throughout his life; he produced a total of 789 papers and seven books during his lifetime. Within three years he became a professor at the Polytechnique, won the Grand Prize of a contest sponsored by the Institute de France for his theory of waves, and was appointed to France’s Academy of Sciences.

In the 1820s Cauchy conducted his most important work He focused on the calculus—also known as complex analysis—in order to simplify, clarify, and systematize its rules. He compiled his lessons and lectures on the subject in three treatises published in the 1820s in which he established the concept of limits and proposed theories of convergence, continuity, derivatives, and integrals. During the same period he developed theoretical details of the functions of complex variables, those using a multiple of the square root of minus one.

In 1830 King Charles X was exiled. Cauchy had been loyal to King Charles and so, rather than swear allegiance to the new King, he exiled himself and ended up teaching in Turin, Italy. Cauchy returned to the Polytechnique in 1838, when an oath of allegiance to the state was no longer a requirement for serving on the faculty. Ten years later he also joined the faculty of the Sorbonne. In 1852 Napoleon III reinstated the requirement of the oath but excused Cauchy from having to take it. Cauchy’s response was to donate his salary to the poor of his home town. Cauchy died on May 23, 1857, in Sceaux, France.

**AugustinLouis Cauchy’s Legacy**

Cauchy made contributions in various fields of mathematics, but his legacy rests primarily on his systemization of the calculus and his refinement of the theory of complex variables.

In developing and systematizing the concepts, symbols, and theorems of the calculus, Cauchy gave mathematics a powerful tool for solving problems in science and engineering, NIELS HENRIK ABEL reacted as if he’d had a religious conversion after reading Cauchy’s published lecture notes. He used Cauchy’s method in his own mathematical work on infinite series. Bemhard Riemann was also directly affected and, with Karl Weierstrass, extended Cauchy’s work to complex function theory. Later Georg Cantor, Richard Dedekind, Eduard Heine, and Weierstrass developed the modern theory of real numbers. The favorable intellectual climate to make all this possible was created by Cauchy, the sometimes aloof professor who threw away seminal papers sent to him by young admirers like Abel.

For the next hundred years calculus textbooks were almost exclusively based on Cauchy’s method and proofs. No other mathematician has had so many concepts and theories beating his name, but perhaps no other ever examined the foundations of his discipline so rigorously and attempted such a comprehensive and creative reorganization of it.

His theory on complex variables is now invaluable in the several fields of applied mathematics, including applications in physics and aeronautics.

Augustin Louis Cauchy – 1789-1857