My first programming role was on the back of work by an engineer in this article. The core of the solver was a FORTRAN implementation of a paper on p-convergence. It was really amazing seeing our software predict how a small crack in a part of an aircraft would propagate. The 3D model produced matched the photograph shared later.
The lead developer (at the time) once said that the biggest software failure we can have is not incorrect results, but incorrect results without the user knowing. This is probably why I am so bothered by silent failures in my big company role now.