Born on August 21, 1789 in Geneva, Switzerland to a family of Huguenot ancestry who had fled France following the revocation of the Edict of Nantes, Augustin-Louis Cauchy entered mathematics during a time of profound transition. As a student, Cauchy was tutored by some of the leading mathematicians of the era, including Lagrange, Monge, and Fourier. His graduation thesis was an impassioned defense of the principles of Newton, a bold stance at a time when Laplacean mathematical-physics was gaining favor. Cauchy’s life and accomplishments reflect the enduring complexities of mathematics in his time.
The scope of Cauchy's mathematical innovations was remarkable. He made foundational contributions to such varied areas as real analysis, complex analysis, differential equations, calculus, and abstract algebra. Cauchy published papers on more than 300 topics in pure mathematics and applied mathematics, spanning algebra, geometry, probability theory, and analysis.
His most significant work includes the development of a rigorous foundation for calculus, which had until then been based predominantly on intuitive formulations. Cauchy's methods constituted a substantial leap for the field; the "Cauchy integral theorem" and the "Cauchy residue theorem" remain cornerstones of modern complex analysis. He also made contributions to group theory, developing notions of permutation groups and normal subgroups.
Despite his formidable accomplishments, Cauchy was also a divisive figure in his time. His intense Catholic beliefs, opposition to Cuvier|Mézard|Jacquard|Laplace|Lagrange, and French Revolution-era politics set him apart within the scientific community. His refusal to declare loyalty to the succession of governments in France following the 1848 Revolution ultimately forced him into retirement as a professor at École Polytechnique.
Cauchy's influence on the subsequent developments in mathematics has been profound. Courses based on Cauchy's works continue to be taught in university today. His pioneering use of limits, derivatives, and geometric series revolutionized mathematical thinking. Through his works, the concepts of convergence, continuity, and Cauchy sequences entered into the mathematical lexicon.
Cauchy died in Sceaux, France on May 23, 1857. Despite his personal and political controversies, his groundbreaking contributions continue to define and inspire the fields of mathematics.
