Mathematicians use their advanced knowledge of numbers and science to solve theoretical problems, evaluate experiments and surveys, and develop practical statistics to be used in engineering and business. Most experts specialize in either theoretical research or applied mathematical studies. Mathematician jobs can be found in a large number of different settings, including research institutions, industries and businesses, government agencies, military branches, and universities.
Theoretical and research mathematician jobs entail developing new equations and formulas, solving longstanding conundrums, and proposing theories which explain natural phenomena. Many mathematicians work in research laboratories at private institutions and universities, examining previous research and working tirelessly to find meaningful relationships between numbers and theories. An expert commonly spends months or even years trying to prove a theory or develop a new mathematical concept. Theoretical mathematicians often write detailed scientific papers about their work and present their findings to other experts in the field. Many professionals choose to become university professors, teaching number theory and research techniques to the next generation of mathematicians.
Professionals who specialize in applied mathematics research and develop new equipment and products, architectural designs, and business plans. Mathematician jobs in industrial or business settings might involve using math and statistics to create efficient manufacturing systems, marketing techniques, or computer programs. Engineering firms commonly hire mathematicians to calculate measurements for the safest and most practical designs of different structures, such as skyscrapers, tunnels, and bridges. Individuals who find employment with geological and environmental organizations analyze trends in volcanic or seismic activity, explain plant and animal behavior, predict weather patterns, and determine pollution levels in a given area.
There is a strong demand for skilled mathematicians in various government agencies and military posts. Many experts apply their knowledge of mathematical principles to the development of more precise weapons and military strategies. Highly skilled mathematicians may be asked to translate coded messages or break ciphers that have been intercepted from enemies. Federal space agencies, such as the National Aeronautics and Space Administration in the United States, hire experts to help design satellites and spaceships, determine appropriate flight paths and trajectories, and analyze the risks involved in space missions.
To obtain most mathematician jobs, individuals must usually hold a PhD. Intensive classroom training in theoretical or applied mathematics is essential to developing the skills needed in future careers. Many doctoral students specialize in a specific mathematical field, such as statistical or economical analysis, to prepare them for mathematician jobs in government or industry. Those who plan on teaching at colleges and universities may also choose to take extensive education and communications courses.
anon40817 Post 3 
Mathematicians help insurance companies determine how long people will live, how many may be hurt in accidents in a year, how often a house burns. This type of mathematician is called an Actuary, and they usually deal with projections into the future based on data from the past. It is possible to calculate the probability of most any happening in the future, if there is enough data from the past to use as a guide. The more data, the more accurate these predictions become. Many other companies also use actuarial models for predicting the future. Marketing companies or departments use purchasing data for forecasting next year's sales, favorite colors, home purchases, etc. Knowing the future of something is vital to our lives, so the more we know about yesterday, the more we will know about tomorrow.

anon40816 Post 2 
Mr. Jeffries forgot to mention Poker player. 
anon40815 Post 1 
Mathematicians also translate sonar and other reflective scans into 3dimensional representations of the area scanned. For example, boats tow sonar equipment behind them when looking for gas and oil deposits under water. The sonar readings change if it travels from solid rock to something more liquid. These readings can be analyzed by computer programs that produce 3D drawings of the area. Imagine a knife had been sliced into the earth, and you were at the side. Quite often, gas and oil are found in structures shaped like a dome, with the gas trapped at the top above the oil. The data collected will also tell how far beneath the ground the gas and oil are located, how large the area
is, if it's leaking out or being tapped by an existing well. A variety of info can be known by the speed at which the sound wave travels through the ground and bounces back to the sonar equipment.
Any job that requires the interpretation of numbers can be done by a properly trained mathematician, although people who deal with numbers which represent money usually call themselves accountants. 