Not necessarily, and in fact this view can be easily refuted when one observes the broad spectrum of careers in which a mathematician can work. It is forgivable to believe that mathematicians mainly work in educational settings though, because many are given job titles from the fields in which they work and so are not technically termed ‘mathematicians’.
A mathematician can specialize in areas as divergent as actuary, where they will use their skills to undertake risk analysis and build mathematic models, or meteorology, where they can analyze data using mathematical principles.
Of course, some mathematicians do pursue careers in research and teaching, but there are certainly other avenues for mathematicians to follow.
