A woman writing math equations on a transparent board

A mathematician could...

Design and decipher codes to help our military and intelligence agencies securely transmit and retrieve sensitive information. Digital image of a magnifying glass magnifying rows of random numbers and letters on a screen Predict how fast tumors will grow and how well chemotherapy can shrink them, using a mathematical model. A ball made of multi-colored patches on a graph
Mathematically model interactions between different animals to understand how the extinction of one species will impact the food chain. A bear standing in a river holds a fish in its mouth Develop a mathematical model to predict tsunamis that develop after underwater sediment avalanches. Digital image of large waves moving towards a beach
Find out more...

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 abstract-thinking 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, pre-calculus, calculus, English; if available, statistics
Median Salary
U.S. Mean Annual Wage
Min Wage
Projected Job Growth (2014-2024) Much Faster than Average (21% or more) In Demand!
  • Read this interview to meet Karen Amanda Yeats who loves theoretical mathematics.
  • MIT professor Kiran Kedlaya is a mathematician, a juggler, a singer, a bicyclist, and a photographer, but most of all, he is a puzzler.
  • Read this interview to meet Dr. Bonita Saunders, an applied mathematician who is working to solve problems in science and engineering, and who also enjoys teaching math to students of all ages.
  • Meet Andrew Wiles, the man who solved Fermat's Last Theorem.
Related Occupations
  • Cost estimators
  • Compensation, benefits, and job analysis specialists
  • Insurance underwriters
  • Operations research analysts
  • Statisticians
  • Mathematical technicians
  • Statistical assistants
  • Traffic technicians
Source: O*Net

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, entry-level 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.

Watch this video to see how mathematicians create the animated characters and amazing graphics in movies.

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 cost-effectiveness 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 enforcement-related 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 law-enforcement-related information in code.
  • Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.

Source: BLS

Companies That Hire Mathematicians

Explore what you might do on the job with one of these projects...

Science Fair Project Idea
Juice boxes are so convenient—just poke the straw in and sip away! But have you ever noticed that some juice boxes don't seem to have much juice, even when they have a lot of packaging? It might surprise you how much thought goes into the design and manufacturing of a juice box. Each manufacturer has carefully calculated how big each side should be to hold a certain amount of juice inside. In this science project, you will find out how different brands of juice measure up. Read more
Science Fair Project Idea
You might think that one sure-fire way to keep your computer safe from hackers is to disconnect it from the internet entirely. But did you know that even without internet, a computer can transmit data using light, sound, vibrations, or even heat? In this project, you will investigate how a spy or hacker can steal data from an "air-gapped" computer that has no internet connection. You can even use Google's Science Journal app to demonstrate how the data can be picked up by a nearby smartphone. Read more
Science Fair Project Idea
Why do the planets orbit the sun without flying off into space? Do they move in perfect circles or do their orbits take a different shape? And how could you possibly do a science project about any of this—you can't do an experiment with the planets! However, you can build a model of our solar system that demonstrates the concept of gravity, using balls of different sizes to represent the sun and planets. Watch this video for an excellent introduction to the model: … Read more
Science Fair Project Idea
Did you know that you can figure out how much sugar is in a liquid without ever tasting it? In this science fair project, you will learn how to measure the concentration of sugar dissolved in a liquid by using a laser pointer, a hollow prism, and some physics. You will discover how refraction, or the bending of light, is the key to measuring the sugar content of a liquid with a laser pointer. Read more
Science Fair Project Idea
Everyone has experienced the warmth provided by a shaft of sunlight through a window. In this physics science fair project, you will determine how the color of an object affects the amount of radiant energy that is absorbed. You will then use the Stefan-Boltzmann equation to determine the amount of energy that is absorbed and re-emitted by the different colors. Read more
Science Fair Project Idea
In physics class, you have probably rolled your eyes at some point after being assigned a "projectile motion" homework problem where you use equations to predict how a ball will move through the air. This experiment will show you just how fun that problem can be by using a real catapult to launch a ball and videotaping it as it flies along its path. Then, you will analyze the video and compare it to what the equations predicted. If you have ever wondered if those equations in your physics… Read more
Science Fair Project Idea
Would it surprise you to learn that no one knows the exact age of the universe? Astronomers have estimates, and as they gather increasingly precise data and measurements, they continue to refine those estimates to come up with more accurate estimates. In this project, you can look at data about stars in dense groups called globular clusters and come up with your own estimate for the minimum age of the universe. How closely will your estimate match those of other astronomers? Read more
Science Fair Project Idea
Have you ever seen a geodesic dome? Geodesic domes are approximately sphere-like (or partially sphere-like) structures made up of interconnected triangles. A famous geodesic dome is Spaceship Earth at EPCOT in Walt Disney World, Florida, but geodesic domes are also commonly found as climbing domes at playgrounds. In this science project, you will get to build a geodesic dome using rolled-up newspapers and tape. How much mass do you think your dome will be able to support? Build one and find out! Read more
Science Fair Project Idea
A kaleidoscope is a fun toy that creates amazing images when you look into it. Wouldn't it be fun to create those images yourself? Check out this project to learn how to build your own kaleidoscope and to learn how the inside of a kaleidoscope works. Then you can create and adjust your own amazing, colorful images! Read more
Science Fair Project Idea
You can measure the diameter of the Sun (and Moon) with a pinhole and a ruler! All you need to know is some simple geometry and the average distance between the Earth and Sun (or Moon). An easy way to make a pinhole is to cut a square hole (2-3 cm across) in the center of a piece of cardboard. Carefully tape a piece of aluminum foil flat over the hole. Use a sharp pin or needle to poke a tiny hole in the center of the foil. Use the pinhole to project an image of the Sun onto a wall or piece… Read more
Science Fair Project Idea
How big a ruler would you need to measure the circumference of the Earth? Did you know that you can do it with a yardstick? (And you won't have to travel all the way around the world!) Read more
Science Fair Project Idea
Water striders (also called water bugs, pond skippers, etc.) are insects that can hop around on the surface of water (Figure 1). Unlike boats or other floating objects that are partially submerged and held up by the resulting buoyant force, water striders are held up by surface tension. Figure 1. Water striders (image credit Isaka Yoji). You can build your own water striders using thin wire (Figure 2 and following video). Do some background research… Read more
Science Fair Project Idea
If you like solving challenging puzzles, this could be a good project for you. In this project you will research different methods for solving a Rubik's cube, and then do an experiment to compare them to each other. Which method works fastest? Read more
Science Fair Project Idea
You are right next to the basket and someone passes you the ball. Will you go for a direct shot or will you use the backboard and take a bank shot at the basket? Would different positions on the court give you a higher chance of making a shot using the backboard than others, even when keeping the distance from the hoop the same? In this science project, you will build a scale model and test different positions on the court to determine if one results in a better chance of making a bank shot… Read more
Science Fair Project Idea
There is evidence to be gathered at every crime scene. The hard part is making sense of it all. That's where crime scene investigators and forensic scientists come in. In this science fair project, you will investigate blood spatter using fake blood. Your job, as an impartial scientist, is to deliver facts so that justice can be served. Are you up to the challenge? Read more
Science Fair Project Idea
Many things in nature are periodic: the seasons of the year, the phases of the moon, the vibration of a violin string, and the beating of the human heart. In each of these cases, the events occur in repeated cycles, or periods. In this project, you will investigate the periodic motion of a spring, using a mini Slinky®. You can also measure the motion of your spring using Google's Science Journal app. Basic physics will then allow you to determine the Hooke's Law spring constant. Your… Read more
Science Fair Project Idea
You've probably noticed the colorful patterns "reflecting" from the shiny surface of a CD disk. What you are seeing is actually diffraction of white light, and the rainbows of color are diffraction patterns. In this project you'll learn about how diffraction patterns are generated, and you'll find out how you can use a laser pointer and a protractor to measure the microscopic spacing of data tracks on a CD. Read more
Science Fair Project Idea
This project challenges you to figure out how to make geometric patterns with Rubik's Cube. Leaving your cube in one of these positions makes it much more tempting to pick it up and 'fix' it. Can you figure out how to make a checkerboard, or a cube-within-a-cube? Can you make only the center piece a different color from the rest? Can you figure out how to solve the cube from these positions? Read more
Science Fair Project Idea
Big data is one of the most promising and hyped trends in technology and business today. Big data refers to data-analysis jobs that are too large and complex to be analyzed by applications that are traditionally used. Big data sets hold valuable information. Many publicly available data sets have the potential to improve our everyday lives by giving us insight into the things we care about. How well-equipped are we to extract information from the data? Visualizations and aggregations (or… Read more
Science Fair Project Idea
Have you ever used a toy like a Spirograph® to draw precise, repeatable patterns on a piece of paper? What if you could use a computer to automatically draw the patterns for you? This project will show you how to do just that using the Raspberry Pi Projects Kit. Check out the video to see what this simple, but fun, project looks like: … Read more

Ask Questions

Do you have a specific question about a career as a Mathematician that isn't answered on this page? Post your question on the Science Buddies Ask an Expert Forum.

Additional Information


Additional Support

We'd like to acknowledge the additional support of:

  • Chevron
  • Motorola Solutions
  • Northrop Grumman
Free science fair projects.