A reason to learn Fortran besides the ability to write stand-alone programs is the ability to extend other languages or programs with a function or subroutine. This is often done to extend general-purpose languages such as Python, R, and Matlab. At GitHub I see a number of projects that extend specialized codes such as Abaqus and LS-Dyna. What are some others? A web page at Fortran-lang could list such programs and explain that even a modest proficiency in Fortran can enable you to attack difficult problems.
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FORGE is a FEM software for material forming simulations. Users can extend its functionalities with Fortran user-routines >> Generate its own user routines in FORGE®
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Some time ago I wrote several examples of how to call fortran from Matlab using MEX.
A example is using interpolation. Interpolation (even linear interpolation) is typically a bottleneck in Matlab codes, so it is efficient to write a subroutine in Fortran, compile it with mex and then call it from within your matlab program
Here is the link: GitHub - aledinola/MEX: Matlab - Fortran using MEX
Comments and suggestions are welcome!