An omnipresent legacy
If summarizing Cauchy's multifaceted work is difficult, detailing the extensions to which his work has given rise to is impossible, so profound has his influence been. Cauchy's name is absolutely everywhere in higher mathematics: Cauchy's criterion, Cauchy's distribution, Cauchy's problem, the Cauchy-Schwarz inequality, not to mention of course the various Cauchy theorems. All these denominations bear witness to a legacy that has permeated all of mathematics. And if it happens that, thinking of one or another of the great figures of his era, the names of Galois or Gauss come first to mind, Baron Cauchy is no less one of those rare mathematicians of whom it can be said that, in all fields, there is a before and an after him.
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A distribution like no other
Standard probability distributions can sometimes be far removed from what is observed. When extreme cases occur too often, the Cauchy distribution comes into its own.
Inflating polyhedra
In his early work, Cauchy revived the study of polyhedra. Ever since his results on the rigidity of convex polyhedra, mathematicians have sought to learn more about more general cases. The quest has produced a new concept, the flexahedron, and a fascinating property: the bellows theorem.
Origins of group theory: Cauchy and Galois | Tangente
Cauchy the analyst is well known; Cauchy the algebraist, much less so. Cauchy's contribution to group theory long went unrecognized, even though his research on algebraic structures was highly influential.
Complex analysis in fluid mechanics | Tangente
When Cauchy, ever the theoretician, developed complex analysis, he could hardly have imagined that his results would lead to so many powerful methods for designing aircraft wings or studying fracture mechanics.
How Cauchy saw the world: science and faith | Tangente
In a series of lectures, Cauchy reveals his vision of the real world through the science of his day. They reveal a scholar wrestling with his religious convictions.