Reusable rockets were "invented" by Lars Blackmore when he was working at JPL (Jet Propulsion Lab). I say invented because like anything in the evolution of engineering, credit is messy.

https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory

> Founded in 1936 by California Institute of Technology (Caltech) researchers, the laboratory is now owned and sponsored by NASA and administered and managed by Caltech.

Minimum-Landing-Error Powered-Descent Guidance for Mars Landing Using Convex Optimization http://larsjamesblackmore.com/BlackmoreEtAlJGCD10.pdf

Elon originally wanted parachutes and was convinced by Lars to go with self landing rockets.