In terms of examples of hard sciences where it shines: It is the only tool in existence that has at the same time high-quality differential equation solvers and autodiff on them. Compare DifferentialEquations.jl to any other package in any other language. The rich capabilities of the aforementioned package depend on the multiple dispatch + aggressive devirtualization used in Julia. Python/Jax/Tensorflow/Pytorch while wonderful on their own, are nowhere near these capabilities. Matlab/Mathematica do not have these capabilities. The famous C/Fortran/C++ libraries are also far less capable in comparison.