I'm curious how did mathematics miss out on the word "science." The meaning of the word "scientist" is consistent with how it's not ascribed to a mathematician as mathematicians don't do anything related to the scientific method.

The thing is you stated that around this time the term "science" was more broad and just meant acquiring knowledge... how come "science" wasn't applied to mathematicians? Technically, according to what you stated, the definition was broad enough to apply to mathematicians.