I have a PhD in mathematics, and have been working in the public sector (NASA) for a little under 10 years. A mix of interest in numerical linear algebra and software engineering helped me work into a niche in scientific computing and engineering software development.

Math is a very, very broad professional interest area. It branches into education, academia, and several areas in several industries around the senior year of an undergraduate program. I'd recommend undergraduate math majors try and get into co-op or paid internship programs as soon as they feel comfortable with it. But that's advice that I'd also give to ANY student these days.

Most technical organizations will hire folks with a mathematics background or entertain the though for a promising applicant. But there are almost no job titles out there called "Mathematician". That can be confusing to some.