A mathematician could...
Design and decipher codes to help our military and intelligence agencies securely transmit and retrieve sensitive information.  Predict how fast tumors will grow and how well chemotherapy can shrink them, using a mathematical model.  
Mathematically model interactions between different animals to understand how the extinction of one species will impact the food chain.  Develop a mathematical model to predict tsunamis that develop after underwater sediment avalanches. 
Key Facts & Information
Overview  Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering.  
Key Requirements  Excellent spatial, analytical, and abstractthinking skills, along with the ability to communicate with a variety of scientists and engineers  
Minimum Degree  Bachelor's degree  
Subjects to Study in High School  Physics, computer science, geometry, algebra II, precalculus, calculus, English; if available, statistics  
Median Salary 


Projected Job Growth (20122022)  Much Faster than Average (21% or more)  
Interview 


Related Occupations 

Training, Other Qualifications
A PhD degree in mathematics usually is the minimum educational requirement for prospective mathematicians, except in the federal government.
Education and Training
In the federal government, entrylevel job candidates usually must have at least a bachelor's degree with a major in mathematics, or 24 semester hours of mathematics courses. Outside the federal government, bachelor's degree holders in mathematics usually are not qualified for most jobs, and many seek advanced degrees in mathematics or a related discipline.
Most colleges and universities offer a bachelor's degree in mathematics. Courses usually required for this degree include calculus, differential equations, and linear and abstract algebra. Additional courses might include probability theory and statistics, mathematical analysis, numerical analysis, topology, discrete mathematics, and mathematical logic. Many colleges and universities advise or require students majoring in mathematics to take courses in a closely related field, such as computer science, engineering, life science, physical science, or economics. A double major in mathematics and another related discipline is particularly desirable to many employers. High school students who are prospective college mathematics majors should take as many mathematics courses as possible while in high school.
In private industry, candidates for mathematician jobs typically need a PhD, although there may be opportunities for those with a master's degree. Most of the positions designated for mathematicians are in research and development laboratories, as part of technical teams.
In 2007, there were more than 300 graduate programs, offering both master's and doctoral degrees, in pure or applied mathematics around the country. In graduate school, students conduct research and take advanced courses, usually specializing in a subfield of mathematics.
Other Qualifications
For jobs in applied mathematics, training in the field in which mathematics will be used is very important. Mathematics is used extensively in physics, actuarial science, statistics, engineering, and operations research. Computer science, business and industrial management, economics, finance, chemistry, geology, life sciences, and behavioral sciences are likewise dependent on applied mathematics. Mathematicians also should have substantial knowledge of computer programming, because most complex mathematical computation and much mathematical modeling are done on a computer.
Mathematicians need to have good reasoning to identify, analyze, and apply basic principles to technical problems. Communication skills also are important, as mathematicians must be able to interact and discuss proposed solutions with people who may not have extensive knowledge of mathematics.
Nature of the Work
Mathematics is one of the oldest and most fundamental sciences. Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems. The work of mathematicians falls into two broad classes—theoretical (pure) mathematics and applied mathematics. These classes, however, are not sharply defined and often overlap.
Theoretical mathematicians advance mathematical knowledge by developing new principles and recognizing previously unknown relationships between existing principles of mathematics. Although these workers seek to increase basic knowledge without necessarily considering its practical use, such pure and abstract knowledge has been instrumental in producing or furthering many scientific and engineering achievements. Many theoretical mathematicians are employed as university faculty, dividing their time between teaching and conducting research.
Applied mathematicians, on the other hand, use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences. For example, they may analyze the most efficient way to schedule airline routes between cities, the effects and safety of new drugs, the aerodynamic characteristics of an experimental automobile, or the costeffectiveness of alternative manufacturing processes.
Applied mathematicians working in industrial research and development may develop or enhance mathematical methods when solving a difficult problem. Some mathematicians, called cryptanalysts, analyze and decipher encryption systems—codes—designed to transmit military, political, financial, or law enforcementrelated information. Applied mathematicians start with a practical problem, envision its separate elements, and then reduce the elements to mathematical variables. They often use computers to analyze relationships among the variables and solve complex problems by developing models with alternative solutions.
Individuals with titles other than mathematician do much of the work in applied mathematics. In fact, because mathematics is the foundation on which so many other academic disciplines are built, the number of workers using mathematical techniques is much greater than the number formally called mathematicians. For example, engineers, computer scientists, physicists, and economists are among those who use mathematics extensively. Some professionals, including statisticians, actuaries, and operations research analysts, are actually specialists in a particular branch of mathematics. Applied mathematicians are frequently required to collaborate with other workers in their organizations to find common solutions to problems.
Work Environment
Mathematicians usually work in comfortable offices. They often are part of interdisciplinary teams that may include economists, engineers, computer scientists, physicists, technicians, and others. Deadlines, overtime work, special requests for information or analysis, and prolonged travel to attend seminars or conferences may be part of their jobs.
Mathematicians who work in academia usually have a mix of teaching and research responsibilities. These mathematicians may conduct research alone or in close collaboration with other mathematicians. Collaborators may work together at the same institution or from different locations, using technology such as email to communicate. Mathematicians in academia also may be aided by graduate students.
On the Job
 Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
 Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
 Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
 Perform computations and apply methods of numerical analysis to data.
 Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
 Assemble sets of assumptions and explore the consequences of each set.
 Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
 Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
 Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or lawenforcementrelated information in code.
 Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
Companies That Hire Mathematicians
Explore what you might do on the job with one of these projects...
 A Matter of Time
 Around the World: The Geometry of Shooting Baskets
 Balls Bouncing Off of Surfaces
 Basketball: The Geometry of Banking a Basket
 Buoyancy of Floating Cylinders
 Calculating the Circumference of the Earth
 Catch the Wave!
 Chain Reaction: Inversion and the Pappus Chain Theorem
 Crystal Ball Math: Predicting Population Growth with Models
 Digital Image Processing
 Digital Photos and Dynamic Range
 Divide and Conquer: Proving Pick's Theorem for Lattice Polygons
 Dome Sweet Dome
 Dots Per Inch (DPI) and Image Quality
 Encryption
 Estimation and Population Size
 Exploring Fractals
 Football Punting: Distance vs. Hangtime
 Football: Punting
 Fractals
Ask Questions
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Additional Information
 American Mathematical Society: www.ams.org
 Society for Industrial and Applied Mathematics: www.siam.org
Sources
 O*Net Online. (2009). National Center for O*Net Development. Retrieved May 1, 2009, from http://online.onetcenter.org/
 Nova. (2000, November). Solving Fermat: Andrew Wiles. Retrieved September 4, 2009, from http://www.pbs.org/wgbh/nova/proof/wiles.html
 Thompson, A.H. (2006, November 27). Interview with Kiran Kedlaya, Mathematician and Puzzler.Retrieved September 4, 2009, from http://www.cogito.org/interviews/InterviewsDetail.aspx?ContentID=11134
 Sloan Career Cornerstone Center. (n.d.). Bonita Saunders. Retrieved September 4, 2009, from http://www.careercornerstone.org/math/profiles/saunders.htm
 MathMania. (1999, February). Interview with a Mathematician. Retrieved September 4, 2009, from http://www.edu.uwo.ca/mpc/files/Yeats.pdf
 ScienceDaily. (2009). Math in the Movies: Mathematicians to Thank for Great Graphics. Retrieved April 7, 2014, from https://www.youtube.com/watch?v=fxZLnCc1hkM
 Cogito. (2007, May 11). Cogito Interview: Terence Tao, Mathematician and Fields Medalist. Retrieved September 4, 2009, from http://www.cogito.org/Interviews/InterviewsDetail.aspx?ContentID=16579
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