There are so many great careers in mathematics that you can find with a math major.
Introduction to the field:
One you become a mathematician, you will work either in applied mathematics, or theoretical mathematic. Sometimes, theoretical mathematics is referred as pure mathematics.
Gauss, Einstein, and Cauchy were great mathematicians. Gauss is probably the greatest ever.
There is something common with them. They all conduct research extensively.
Those who work in applied mathematics try to learn more about what math has to tell us or how math can be applied in almost any areas of life, such as economics, social science, engineering, biology and many others.
This means that they must find mathematical models that can be used to solve real-world problems.
Those in pure mathematics just want to know more. They are the one who are going to come up with new axioms, definitions, and theorems.
Then, they will devote their lives in proving those theorems. Throughout history they have given us many great achievements that have had profound effects in engineering, science and many other discipline.
Needless to say that one needs to be very good at math to become a mathematician.
Above all, a passion and a love for math are a must. I know some folks who are good at mathematics, yet they certainly do not want to do it everyday.
Mathematicians do math everyday and they are expected to come up with solid proofs for theorems and good mathematical models of real-world problems, and it can be rewarding when one has discovered something.
How to Be a Good Mathematician: 6 Steps - wikiHow