> "How do I capture this extremely complicated real world semantics in code?" and languages can't really solve that

This isn't true. It's possible to write a symbolic differentiation system using, primarily, Scala's type system. In an elegant fashion.

Similarly, Julia represents math better than, say python or Java. A vector type should not need to know about inner products of vectors, because the math definition of a vector space does not.

This will have large effects on how easy it is to decompose your code into neat little pieces.