One can refer to oneself as a mathematician without a degree in maths. One simply has to be a mathematician to refer to onself as a mathematician. The question, however, is what "to be a mathematician" means. Those who aren't paid to teach maths are typically qualified with the title "amateur mathematician" -- as professional mathematicians take the title seriously. Those who get serious publication of their theorems -- amateur or not -- tend to lose the "amateur" -- nobody gets paid to publish in those journals. I was once publicly chastised for calling myself a novelist. I've written novels and had them published (two of which under standard publishing agreements), and the word "novelist" means "one who writes novels" -- so publication was not even in the equation. As the saying goes: "As long as they don't call me late for dinner."