Usefulness of Differential Geometry
If you found Structure and Interpretation of Computer Programs interesting, you might like Functional Differential Geometry (It's from the same authors) .

Differential geometry is deceptively simple. It is surprisingly easy to get the right answer with unclear and informal symbol manipulation.  To address this problem we use computer programs to communicate a precise understanding of the computations in differential geometry.  Expressing the methods of differential geometry in a computer language forces them to be unambiguous and computationally effective. The task of formulating a method as a computer-executable program and debugging that program is a powerful exercise in the learning process.  Also, once formalized procedurally, a mathematical idea becomes a tool that can be used directly to compute results.

Taken from Sussman, Wisdom: Functional Differential Geometry