Mathematicians

• Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
• 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.
• Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
• Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
• Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
• Perform computations and apply methods of numerical analysis to data.
• Develop new principles and new relationships between existing mathematical principles to advance mathematical science.

Source: O*NET OnLine information for Mathematicians.

• Critical Thinking - Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
• Complex Problem Solving - Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
• Reading Comprehension - Understanding written sentences and paragraphs in work related documents.
• Active Learning - Understanding the implications of new information for both current and future problem-solving and decision-making.
• Writing - Communicating effectively in writing as appropriate for the needs of the audience.
• Active Listening - Giving full attention to what other people are saying, taking time to understand the points being made, asking questions as appropriate, and not interrupting at inappropriate times.
• Science - Using scientific rules and methods to solve problems.
• Systems Analysis - Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.
• Speaking - Talking to others to convey information effectively.

Source: O*NET OnLine information for Mathematicians.