# Mathematicians

## At a Glance

- Usually specialize in theoretical or applied math
- Theoretical mathematicians study ideas or theories
- Applied mathematicians use math to solve problems
- Work alone most of the time
- May travel to attend conferences or seminars
- Most have at least a master's degree

## Career summary

Mathematicians study and research numbers. They create new theories and try to solve problems using those theories.Mathematical work falls into two classes:

- Theoretical
- Applied

Theoretical mathematicians study and test new mathematical ideas or theories. They try to find connections between existing theories. The discoveries made by theoretical mathematicians may advance areas such as science or engineering.

Theoretical mathematicians may study:

- Algebra
- Geometry
- Number theory
- Logic

Applied mathematicians use math theories to solve problems. For example, mathematicians study mathematical studies of the effects of new drugs on disease. They analyze numbers to predict how the drugs will impact diseases.

They also study ways to apply math to:

- Science
- Engineering
- Economics
- Computers

Mathematicians may discuss research problems with people in other fields to gain more information. Sometimes they serve as consultants for other researchers. Some mathematicians teach at the college or university level. If they have a teaching certificate they can teach in high school.

Other people who work with math and numbers are statisticians, actuaries, and operations research analysts. They focus on a single area of math.

## Related careers

This career is part of the Science, Technology, Engineering, and Mathematics cluster of careers.

Related careers include:

- Actuaries
- Astronomers
- Computer Programmers
- Economists
- Operations Research Analysts
- Physicists
- Statisticians

## Job duties

### Task list

The following list of tasks is specific to mathematicians.

- Develop mathematical and statistical models.
- Study and test ideas and alternative theories for problem-solving.
- Conduct research using theory in specific areas of math, such as algebra, geometry, number theory, and logic.
- Think of how to apply math to a variety of fields, such as science, engineering, and economics.
- Apply mathematics or mathematical methods of numerical analysis.
- Operate calculators and computers to analyze information.
- Act as consultants to researchers about mathematical methods and applications.
- Keep skills and knowledge up to date by reading journals and attending conferences.

### Common work activities

Mathematicians perform the following tasks. These tasks are common to many careers.

- Use computers
- Analyze data or information
- Make decisions and solve problems
- Think creatively
- Get information needed to do the job
- Process information
- Update and use job-related knowledge
- Communicate with supervisors, peers, or subordinates
- Document and record information
- Estimate sizes, quantities, time, cost, or materials needed
- Identify objects, actions, and events
- Explain the meaning of information to others
- Organize, plan, and prioritize work
- Provide advice and consultation to others
- Teach others
- Communicate with people outside the organization
- Develop goals and strategies
- Establish and maintain relationships

## Work requirements

### Working conditions

In a typical work setting, mathematicians:

*Interpersonal relationships*

- Have a low level of social contact. They occasionally talk to coworkers, but work alone most of the time.
- Communicate by e-mail and in person every day. They also use the phone and write letters and memos, but less often.
- Often work as part of a team.

*Physical work conditions*

- Always work indoors.

*Work performance*

- Must be very exact in their work and be sure all details are done. Errors could make their research invalid.
- Make most of their decisions independently. Often their decisions have an impact on their company's or organization's reputation.
- Set most of their daily tasks and goals without talking to a supervisor.
- Work in a moderately competitive atmosphere.

*Hours/travel*

- Usually work 40 hours a week.
- May work overtime to meet deadlines.
- May travel to attend conferences or seminars.
- Generally work a set schedule.

### Physical demands

Mathematicians frequently:

- Sit for long periods of time.

It is important for mathematicians to be able to:

- See details of objects that are less than a few feet away.
- Understand the speech of another person.
- Speak clearly so listeners can understand.

It is not as important, but still necessary, for mathematicians to be able to:

- Use fingers to grasp, move, or assemble very small objects.
- See details of objects that are more than a few feet away.

### Skills and abilities

Mathematicians need to:

*Communicate*

- Understand written information.
- Read and understand work-related materials.
- Understand spoken information.
- Speak clearly so listeners can understand.
- Write clearly so other people can understand.
- Listen to others and ask questions.

*Reason and problem solve*

- Use reasoning to discover answers to problems.
- Follow guidelines to arrange objects or actions in a certain order.
- Combine several pieces of information and draw conclusions.
- Recognize the nature of a problem.
- Analyze ideas and use logic to determine their strengths and weaknesses.
- Understand new information or materials by studying and working with them.
- Notice when something is wrong or is likely to go wrong.
- Think of new ideas about a topic.
- Develop rules that group items in various ways.
- Think of original, unusual, or creative ways to solve problems.
- Recognize when important changes happen or are likely to happen in a system.
- Judge the costs and benefits of a possible action.
- Identify what must be changed to reach goals.
- Concentrate and not be distracted while performing a task.

*Use math and science*

- Use math skills to solve problems.
- Choose a mathematical method or formula to solve problems.
- Add, subtract, multiply, and divide quickly and correctly.
- Use scientific methods to solve problems.

*Work with people*

- Use several methods to learn or teach new things.

*Perceive and visualize*

- Identify a pattern (a figure, object, word, or sound) that is hidden in distracting material.

## Education and training

### Educational programs

The programs of study listed below will help you prepare for the occupation or career cluster you are exploring.

#### Programs of study directly related to this occupation

#### Other programs of study to consider

### Training

To work as a mathematician, you typically need to:

- have a high school diploma or equivalent;
- have a bachelor's degree; and
- have a graduate degree in mathematics.

#### Education after high school

Most mathematicians have at least a master's degree in math. Course work for this degree includes calculus, differential equations, and abstract algebra. In addition to math, you should take courses in computer science and programming. This is because you use computers for complex calculations and modeling.

You should also consider taking courses closely related to math such as economics, engineering, or physics. A dual major in math and a science is good preparation for an assortment of jobs.

In applied math, it is important to get training in the field in which you will be working. Fields such as business, geology, chemistry, biology, sociology, and psychology all use applied math.

#### Work experience

You should consider participating in an internship while in college. An internship is usually part of a degree program. It offers you a chance to apply what you have learned in the classroom to a work situation. It also allows you to build skills and make contacts with people in the field.

#### On-the-job training

New graduates work under the guidance of experienced mathematicians. Training generally lasts a few months.

### Helpful high school courses

In high school, take classes that prepare you for college. A college preparatory curriculum may be different from your state's graduation requirements . Consider taking as many advanced math classes as you can to prepare for college math courses.

You should also consider taking some advanced courses in high school. This includes Advanced Placement (AP) and International Baccalaureate (IB) courses if they are available in your school. If you do well in these courses, you may receive college credit for them. Advanced courses can also strengthen your college application.

Helpful electives to take in high school that prepare you for this career include:

- Algebra
- Calculus
- Computer Applications
- Probability and Statistics
- Trigonometry

Few mathematicians do just math. Many work in areas such as computer science, engineering, or economics. Consider taking additional electives in areas such as these that interest you.

The courses listed above are meant to help you create your high school plan. If you have not already done so, talk to a school counselor or parent about the courses you are considering taking.

You should also check with a teacher or counselor to see if work-based learning opportunities are available in your school and community. These might include field trips, job shadowing, internships, and actual work experience. The goal of these activities is to help you connect your school experiences with real-life work.

Join some groups, try some hobbies, or volunteer with an organization that interests you. By participating in activities you can have fun, make new friends, and learn about yourself. Maybe one of them will help direct you to a future career. Here are examples of activities and groups that may be available in your high school or community.

## Things to know

Many employers prefer to hire mathematicians who have a doctorate (PhD). Universities choose candidates based on their area of research and the quality of their published articles. For entry-level jobs, the federal government hires applicants who have a bachelor's degree in math.

Employers in research and development often look for applicants who can work well as part of a team. They look for applicants with leadership skills and good oral and written skills. Knowledge of other fields, such as business or marketing, can also be useful.

### Tips

A background in computer science, physics, accounting, or engineering is an important consideration in hiring for some positions. Internships provide valuable work experience. The ability to translate scientific information into non-technical language, both in written form and orally, is also important.

### Costs to workers

Workers may wish to join a professional association, which may have annual dues. Individuals may also be required to pay their own exam fees.

### Job listings

Listed below are links to job categories from the National Labor Exchange that relate to this career. Once you get a list of jobs, you can view information about individual jobs and find out how to apply. If your job search finds too many openings, or if you wish to search for jobs outside of Washington, you will need to refine your search.

To get a listing of current jobs from the WorkSource system, go to the WorkSource website .

## Wages

#Currently, there is no specific statewide wage information available for mathematicians.

Location |
Pay Period | |
||||
---|---|---|---|---|---|---|

10% |
25% |
Median |
75% |
90% |
||

Washington | Hourly | $29.19 | $40.77 | $57.62 | $75.58 | $92.29 |

Monthly | $5,059 | $7,065 | $9,986 | $13,098 | $15,994 | |

Yearly | $60,710 | $84,800 | $119,860 | $157,200 | $191,950 | |

Seattle-Tacoma-Bellevue | Hourly | $29.75 | $47.90 | $69.22 | $85.92 | $100.00 |

Monthly | $5,156 | $8,301 | $11,996 | $14,890 | $17,330 | |

Yearly | $61,869 | $99,627 | $143,981 | $178,712 | $207,992 | |

United States | Hourly | $27.48 | $35.33 | $48.99 | $60.61 | $77.19 |

Monthly | $4,762 | $6,123 | $8,490 | $10,504 | $13,377 | |

Yearly | $57,150 | $73,490 | $101,900 | $126,070 | $160,550 |

Pay varies based on a mathematician's level of education. Mathematicians who have a PhD earn more than those with a bachelor's or master's degree. Pay also varies with the type of industry they work in. Those who work in business tend to earn more than those in government or education.

Mathematicians who work full time usually receive benefits. Benefits may include medical insurance, paid vacation, sick leave, and a retirement plan.

## Employment and outlook

### Washington outlook

The table below provides information about the number of workers in this career in various regions. It also provides information about the expected growth rate and future job openings. This data does not include mathematicians who teach at colleges and universities.

Location | Current employment | Growth over 10 years | Annual openings | |

This occupation |
All occupations |
|||
---|---|---|---|---|

Washington | 145 | 15.2% | 16.1% | 16 |

King County | 75 | 18.7% | 19.6% | 8 |

Snohomish County | 10 | 10.0% | 12.4% | 1 |

United States | 2,900 | 24.1% | 5.2% | 300 |

### National employment

Major employers:

- Federal government agencies
- Research and testing companies
- Technical consulting companies

### National outlook

This occupation will experience large growth in demand, however, it is a very small occupation and not many new jobs will be created. Growth in this occupation will be due to advancements in technology that allow for better collection and processing of data. This will lead to an increased need for mathematicians to analyze the data.

Many jobs that require high levels of math also require knowledge of science. The most common fields in which mathematicians study and find work are computer science and software development, physics, engineering, and operations research. More mathematicians also are becoming involved in financial analysis.

Job openings will occur as mathematicians retire or leave this occupation for other reasons. Job prospects will be best for those with experience in business, computer science, or statistics.

## Other resources

**American Association for the Advancement of Science**

1200 New York Ave, NW

Washington,DC20005

**American Institute of Biological Sciences**

1800 Alexander Bell Drive, Suite 400

Reston, VA 20191

703.674.2500

**American Institute of Physics**

One Physics Ellipse

College Park, MD 20740

301.209.3100

**American Mathematical Society**

201 Charles Street

Providence, RI 02904

800.321.4267

401.455.4000

**Association for the Advancement of Artificial Intelligence**

**IEEE Computer Society**

2001 L Street NW, Suite 700

Washington, DC 20036

202.371.0101

**Mathematical Association of America**

1529 - 18th Street NW

Washington, DC 20036

800.741.9415

202.387.5200

**Mathematical Sciences Career Information**

**National Academy of Sciences Interviews**

**Society for Industrial and Applied Mathematics**

3600 Market Street, 6th Floor

Philadelphia, PA 19104

215.382.9800

**Washington State Science & Engineering Fair**

## References

### Career cluster

### Career path

- Investigative (Science)

### O*Net occupation

### O*Net job zone

Job Zone 5 - Extensive preparation needed. Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience.

### DOT occupation

### Strong Interest Inventory

- Mathematician

### Holland occupational cluster

- Investigative/Conventional/Artistic

### COPSystem

- Science Professional