Just because someone has no formal training in math, and doesn't recognize that what they're doing could be called math, (or strategically refuses to apply the

Just because someone has no formal training in math, and doesn't recognize that what they're doing could be called math, (or strategically refuses to apply the word 'math' to what they do, for sound pedagogical reasons) doesn't mean that they aren't doing math. The cult of the Ph.D. is strong, but you don't actually need some kind of license to think logically about abstract concepts, anymore than a musician needs a formal music education or a cat needs a formal gymnastics education.