Augustin-Louis Cauchy

Augustin-Louis Cauchy was a French mathematician who transformed analysis from an intuitive art into a rigorous science. He gave precise definitions of limit, continuity, and derivative, built the foundations of complex analysis, and left a mark on mechanics and elasticity theory. In terms of the number of theorems named after him, he has no equal.

Biography

Born in Paris at the height of the Revolution, studied at the École Polytechnique and the School of Bridges and Roads. He was a professor at the École Polytechnique, the Sorbonne, and the Collège de France. After the July Revolution, he voluntarily went into exile, worked in Turin and Prague, but later returned. Knight of the Legion of Honour.

Key discoveries

Rigorous definition of limit, continuity, and derivative: replaced intuitive notions with formal definitions in ε-δ language, laying the foundation for modern mathematical analysis.
Cauchy's integral theorem and residue theory: the foundation of complex analysis, enabling the computation of complex integrals and having applications in quantum field theory and hydrodynamics.
Cauchy stress tensor: introduced the concept of a tensor in continuum mechanics, describing the deformation forces inside a body.

💡 Cauchy's incredible prolificness is legendary: he wrote about 800 articles, and the Paris Academy had to limit the volume of publications because the budget could not withstand the printing of his endless works. It is said that his last words were: "Man passes away, but the formulas remain."

Biography

Key discoveries

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