The author seems to be building a false dichotomy. Math is the combination of two. To continue the use of the music analogy, if you can sing and write songs but do not know any theory and cannot express your ideas to anyone but yourself, is it truly music? As an amateur musician, I can say it is absolutely frustrating to work with people who cannot transcribe or manipulate their work in any meaningful way--even a simple tab would do.

Mathematics are the same way. Yes, you need to solve problems, but you also need to solve problems in ways that can build on your past knowledge and be shared with others.

(FYI, I'm a lifelong amateur musician, programmer, and data analyst. My formal education consisted of a double electrical engineering / mathematics major.)