inventions of mathematician Augustin Louis cauthy?

Answer 1

If you mean Cauchy, look him up in Wikipedia.

He worked mainly in analysis -- i.e., glorified calculus. "Cauchy Sequences" were one of the two main contenders for making calculus and real analysis rigorous. He also did important work in probability and complex analysis (calculus of a complex variable), although I forget the details.

He also was an obnoxious French jerk, burying the work of rivals -- famously Evriste Galois -- for decades.

Answer 2

If you mean Cauchy then named after him is an important theorem in the analysis of complex number functions.