Mathematicians
Speciality
Overview
Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve problems in various fields using mathematical methods.
Highlights
Largest undergraduate program (14.7% of workers): Mathematics
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Responsibilities and activities

Mathematicians and statisticians typically do the following:

• Develop new mathematical rules, theories, and concepts in areas such as algebra and geometry
• Decide what data are needed to answer specific questions or problems
• Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, and other fields
• Design surveys, experiments, or opinion polls to collect data
• Develop mathematical or statistical models to analyze data
• Interpret data and report conclusions drawn from their analyses
• Use data analysis to support and improve business decisions

Mathematicians and statisticians apply theories and techniques, such as mathematical or statistical modeling, to solve practical problems. Typically, they work with individuals in other occupations to solve these problems. For example, they may work with chemists, materials scientists, and chemical engineers to analyze the effectiveness of new drugs. Others may work with industrial designers to study the aerodynamic characteristics of new automobiles.

To work on these problems, mathematicians and statisticians must first collect data. Statisticians design surveys, questionnaires, experiments, and opinion polls to collect the data they need. Surveys may be mailed, conducted over the phone, collected online, or gathered through some other means.

Some surveys, such as the U.S. census, include data from nearly everyone. For most surveys and opinion polls, however, statisticians use a sampling method to collect data from some people in a particular group. Statisticians determine the type and size of the sample to be surveyed or polled.

After the data are collected, mathematicians and statisticians use specialized statistical software to analyze data. In their analyses, mathematicians and statisticians identify trends and relationships within the data. They also conduct tests to determine the data’s validity and to account for high survey nonresponse rates or sampling error. Some may help create new software to analyze data more accurately and efficiently.

Mathematicians and statisticians present the findings from their analyses and discuss the data’s limitations in order to prevent inaccurate conclusions from being drawn. They may present written reports, tables, charts, and graphs to other team members and to clients.

Mathematicians and statisticians work in many fields, such as education, marketing, psychology, sports, or any other field that requires the collection and analysis of data. In particular, government, healthcare, and research and development companies employ many statisticians.

Government. Mathematicians and statisticians working in government develop and analyze surveys that collect a variety of data, including unemployment rates, wages, and other estimates pertaining to jobs and workers. Others help to figure out the average level of pesticides in drinking water, the number of endangered species living in a particular area, or the number of people who have a certain disease.

HealthcareStatisticians known as biostatisticians or biometricians work in pharmaceutical companies, public health agencies, or hospitals. They may design studies to test whether drugs successfully treat diseases or medical conditions. They may also help identify the sources of outbreaks of illnesses in humans and animals.

Research and development. Mathematicians and statisticians design experiments for product testing and development. For instance, they may help design experiments to see how car engines perform when exposed to extreme weather conditions. Some may analyze consumer data to help develop marketing strategies and prices for consumer goods.

Colleges and universities. Mathematicians and statisticians working in a postsecondary education institution may study theoretical or abstract concepts in mathematics or statistics. They identify, research, and resolve unexplained issues in mathematics and are concerned primarily with exploring new mathematical or statistical theories to increase knowledge and understanding about the field.

However, the mathematician occupation is a relatively small one, and many people with a degree in mathematics or who develop mathematical theories and models may not be formally known as mathematicians. Instead, they work in related fields and professions. In the computer systems design and related services industries, for example, they may be known as computer programmers or systems analysts. In finance, they may be known as quantitative analysts. Other industries may refer to them as data scientists or data analysts.

Computer and information research scientists, physicists and astronomers, economists, actuaries, operations research analysts, engineers, and many other occupations also use mathematics extensively.

Many people with a Ph.D. in mathematics, particularly theoretical mathematics, work as postsecondary teachers in education institutions. They usually have a mix of teaching and research responsibilities. Some may conduct individual research or collaborate with other professors or mathematicians. Collaborators may work together at the same institution or from different locations.

Salary
Median salary: \$110,860 annually
Half of those employed in this career earn between \$79,280 and \$134,680.
Context: Median Salary
How do salaries for this career compare to other jobs' salaries?
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Salary growth for mathematical scientists
Is this job likely to reward you for sticking with it through pay raises and promotions? The higher a job’s “experience quotient,” the more you are likely to get as you stay there.
Experience quotient percentile
Take a minute to look at how much you might expect your salary to increase with each five years' experience, as well as how the numbers working at each age change. Does this seem to be a job for the young or the old, or could it be a career offering steady salary growth for many years?
Salary distribution
Number employed
How do benefits for this career compare to other jobs? The availability of health care, especially employer provided health care, and pension plans can add significantly to the value of compensation you receive in a career. These charts compare how this career compares to other careers with regard to health care and pension plans.
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Employer is providing health insurance
Employer-provided pension plan is available
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Personality and skills
Can you see yourself in the ranks of Mathematicians? Here are the skills and traits that could lead to success.
Analytical skills
Mathematicians and statisticians use mathematical techniques and models to analyze large amounts of data. They must determine the appropriate software packages and understand computer programming languages to design and develop new techniques and models. They must also be precise and accurate in their analysis.
Communication skills
Mathematicians and statisticians must interact with, and propose solutions to, people who may not have extensive knowledge of mathematics.
Math skills
Mathematicians and statisticians use statistics, calculus, and linear algebra to develop their models and analyses.
Problem-solving skills
Mathematicians and statisticians must devise new solutions to problems encountered by scientists or engineers.
Education pathways to this career
Education attained by mathematicians
According to the Bureau of Labor Statistics (BLS), mathematicians typically hold a master's degree.
Sometimes the typical education identified by the BLS differs a bit from the reality of the how much education current workers actually have. The donut shows the education level held by people currently working as mathematical scientists as reported in responses to the American Community Survey.
Details: Education and training recommended for mathematicians

In private industry, mathematicians typically need an advanced degree, either a master’s degree or a doctorate. For jobs with the federal government, candidates need at least a bachelor’s degree in mathematics or significant coursework in mathematics.

Most colleges and universities offer a bachelor’s degree in mathematics. Courses usually include calculus, differential equations, and linear and abstract algebra. Many colleges and universities advise or require mathematics students to take courses in a related field, such as computer science, engineering, physics, or statistics. Because mathematicians often work with data analysis software, computer programming courses may be particularly beneficial for students.

Many universities offer master’s and doctoral degrees in theoretical or applied mathematics. Many students who get a doctoral degree work as professors of mathematics in a college or university.

Statisticians typically need a master’s degree but some entry-level positions may accept candidates with a bachelor’s degree.

Most statisticians have degrees in mathematics, economics, computer science, or another quantitative field. A degree in statistics typically includes courses in linear algebra, calculus, experimental design, survey methodology, probability, and statistical theory.

Many colleges and universities advise statistics students to take courses in a related field, such as computer science, engineering, or physics. These courses can help prepare students to work in a variety of industries. Coursework in engineering or physical science, for example, may be useful for mathematicians or statisticians working in manufacturing on quality or productivity improvement. A background in biology, chemistry, or health sciences is useful for work testing pharmaceutical or agricultural products.

Because mathematicians and statisticians often work with data analysis software, computer programming courses may be particularly beneficial for students.

Students who are interested in becoming mathematicians or statisticians should take as many math courses as possible in high school.

Education level of Mathematical Scientists
About 54% of mathematical scientists have a graduate-level education, and 91% have at least a bachelor's degree.
Education attained by mathematical scientists
None
High School
Some College
Associate's Degree
Bachelor's Degree
Master's Degree
Professional Degree
Doctorate
Top college degrees
Here are the top college degrees held by the 89% of people in this job who have at least a bachelor's degree. Some of degrees may link to multiple programs due to the way Census classifies college majors. Click on a program to learn more about career opportunities for people who major in that field.
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College majors held by mathematical scientists
This table shows the college majors held by people working as mathematical scientists. If you see "**" before the name of a degree/program, that means this field is one that the Department of Education believes is preparatory for this career. However, you can see from this list that those recommendations are far from your only path to this job!
Major
Salary comparison for bachelor's only
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Career salary (tail) versus Career/Major salary (dot)
Does the bachelor's-only salary rise or fall with this major?
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For people with this career and major
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Education for Career and Major
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Master's
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The link between degrees and this career
With the following sankey diagram, you can follow the top ten bachelor's degrees held by people working as mathematical scientists, and then, in turn, you can see the 10 occupations that hire the most of each degree's graduates. We hope this provides ideas for similar jobs and similar fields of study.
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Where are the jobs
State-by-state employment numbers
Some careers tend to be centered in specific parts of the country. For example, most jobs in fashion are in New York or California. Let's see if your dream job is easy to find in your dream location! We have a few choices for viewing the data that can help you get a full employment picture.
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Number of Mathematical Scientists per 1,000 workers (ACS)
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Job density versus job count
Which states hire the most mathematicians? We wonder if that's a fair question since states come in all sizes, so instead let's start with the question of which states have the highest density of people working as mathematicians. You can choose to view the number of jobs per state if you prefer.
Salaries by state
Let's get a feel for where mathematicians earn the highest salaries. There are several choices for which data we consider and how we view that data, and each can lead to different conclusions, so please read on...
Median salary versus state ratio
We use two methods to compare salaries across states:
• In-state comparisons: the ratio of median (middle) salaries for mathematical scientists compared to the median salary for all people working in each state, or
• Median salary: the unaltered median salaries for mathematical scientists.
We hope the ratio allows perspective about how salaries may compare to the regional cost-of-living.
The darkest shading corresponds to states in which mathematical scientists earn the highest salary when compared to other jobs in the state. We think this figure might be a better indicator than the actual salary for your buying power as a state resident.
Select a state to see local area details
Location-adjusted median salary for Mathematical Scientists (ACS for all specialties)
Employment
8% of Mathematical scientists are working part time.
We’ve found that some jobs have a huge number of part-time workers, and typically that is because they are unable to find full-time work or the job itself can’t provide full-time hours. With 8% part-time workers, this occupation has a lower percentage of part-time workers than 64% of careers.
Employer types
This donut shares the break-down of workers by employer type, giving us a picture of what employers most typically hire for this career.
Employers of undefined (ACS)
Private for-profit
Private not-for-profit
Local government
State government
Federal government
Self-employed incorporated
Self-employed not incorporated
Working without pay
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Distribution: Salaries of mathematical scientists by type of employer
Here are the salary distributions based on employer type.
Gender
Mathematical scientists and gender
With 46% women, this occupation has a higher percentage of women than 58% of careers.
Gender of Mathematical scientists
Men (54%)
Women (46%)
Distribution: salaries by gender
Does gender greatly influence your salary in this career? The closer the bars are, the less discrepancy there is.
We only include salary data when the survey error is less than 20%, so you may see only partial information for some categories.
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Context: Women in the workforce
How does this career compare to other careers with regard to the percentage of women in the career.
Context: Salary inequity
The median salary for all full-time male workers in the US exceeds the full-time median salary for women by 19%. The situation is a little better for mathematical scientists, with the median salary for men 13% higher than the median salary for women.
Race/Origin
Race and origin of Mathematical scientists
This donut shows the distribution of race and origin among those employed as Mathematical scientists.
Race/origin of mathematical scientists
White (67% )
Asian (24% )
Black (6% )
Multiracial (2% )
Other (1% )
American Indian (1% )
Hispanic (0% )
Pacific Islander (0% )
Distribution: salaries by race/origin
Some careers might have a pay disparity based on race or origin, the closer the below bars are the less of a discrepancy is present.
We only include salary data when the survey error is less than 20%, so you may see only partial information for some categories.