The basic skills required for mathematics as a field of study - mainly problem-solving, deductive reasoning and forecasting - can lead to a wide variety of vocations. Math has historically held a "tough and disliked" reputation in academics and has always been thought of as an income-generator only for those who enjoy inquiry and computation.
There is, however, a contemporary need for an "art" of mathematics, for those who have mastered the competencies of math for use in other disciplines rather than simply staying in the science of it. The most traditional (obvious and popular) careers that have emerged for those who study math are teaching, computer science and research. Special reports about the national shortage of teachers have highlighted the fact that math teachers are in high demand.
When we think of computer science, the popular tendency is toward either software (programming) or hardware (troubleshooting mother boards, keyboards and monitors). This field offers so many other possibilities. In our post-9/11 times and with the increased alerts for terrorist threats, a profitable field for mathematicians is cryptology. Special national defense agencies need cryptologists who can break secret codes and prevent loss of life and physical harm. This specialized field is one that will probably stay in high demand. Banks and telecommunications companies also have a pressing need for cryptologists. The security of financial information and the delivery of broadcast media are high priorities for most of our world community. Because we live in a time of fast developing technology, mathematicians are also needed to improve the functions of computerized gadgets, hard drives and the Internet.
Forecasting (or probability) is required for many fields that might not be easily targeted as mathematics-related. Game theory, for example, a statistics laden science that might be used to generate strategies for winning wars, is completely based in mathematics. In the same way, statistics can be used to determine populations affected by epidemics and the rates at which they are affected. Statistics help determine the financial health of the national economy and drive feasibility studies for urban planning. Mathematics also becomes an important skill in the fields of genetics, insurance and actuary science, and foreign language translation.
One of the most interesting career fields in mathematics when combined with physics, is aeronautical engineering. Many astronauts and researchers who work for NASA have specialized in all of these fields. Equally interesting are those who need to be versed in the language of mathematics to either make the findings or writings of mathematics researchers more easily understandable. Career fields that cover translation would be publishers and news reporters who can translate new research for readers.
Because many of the career fields in mathematics require higher degrees (many, the Ph.D.), the average age for an entry-level mathematician is about 28. For those who do not have the Ph.D., the age is probably in the mid-30s, since it takes that long to build experience and credentials.
We are taught from an early age to fear mathematics. Because it involves numbers and not words, it is a language many are not willing to learn. Those who do learn it, though, place themselves in a very lucrative position to be well-paid and frequently sought for their knowledge.