How to Become a Mathematician in 5 Steps

Explore the career requirements for mathematicians. Get the facts about salary, job duties, degree requirements and job outlook to determine if this is the right career for you. Schools offering Mathematics degrees can also be found in these popular choices.

What Does a Mathematician Do?

As a mathematician, there are a number of career paths you could explore. Some mathematicians work as college or university professors, while others may work as research scientists. In both jobs, you will work with mathematical rules and theories and apply these theories to solve problems in a variety of different fields, like engineering and business. Explore some of the specialty areas of this field and review some of the common career details by reading the table below.

Degree Required Bachelor's degree for entry-level, but master's or doctoral degree preferred
Education Field of Study Mathematics, applied mathematics, theoretical mathematics
Key Responsibilities Solve mathematical problems for several industries, such as the government, business, engineering and academia; analyze data and create reports on findings; stay abreast of current math trends
Job Growth (2014-2024) 21%*
Average Salary (2015) $112,560*

Source: *U.S. Bureau of Labor Statistics

What is a Mathematician?

A mathematician is a scholar whose field of expertise is mathematics. They explore abstract theoretical problems or apply mathematical theory to the solution of real world problems in economics, engineering, business, physics and other sciences.

Specific duties might include conducting research and manipulating existing mathematical principles to discover new principles, as well as analyzing data and developing algorithms, computational methods and statistical models to reveal relationships between the data elements. You could also design or decipher encryption systems for military, law enforcement, governmental or business applications. As a scholar, you'll also spend time reading mathematical journals and participating in conferences to stay abreast of developments in the field.

Step 1: Prepare in High School

You should take as many mathematics courses as possible in high school. Most schools offer algebra, trigonometry and geometry. If available, advanced placement courses in calculus and physics can provide you with a sense of what courses in your first year of college will be like. Computer courses are helpful since your later work may involve very large data sets, large equation matrixes or repetitive calculations.

Step 2: Earn a Bachelor's Degree in Mathematics

Bachelor's degree programs in mathematics train you to understand and apply elements of mathematical reasoning like logic, formal proof, abstraction and generalization. You learn to analyze data, create and analyze mathematical models and communicate robust arguments. Course topics may include calculus, linear algebra and differential equations, number theory, numerical analysis, probability and statistics. Bachelor's degrees are typically earned in four years.

Step 3: Enroll in a Ph.D. Program

You may gain admission to most doctoral programs in mathematics with a bachelor's degree, but most require you to complete their requirements for a master's degree on the way to earning a doctorate. Admission to these programs is competitive, with most requiring applicants to submit general Graduate Record Examination (GRE) scores as well as scores for the GRE mathematics subject test. You will probably need to submit letters of recommendation, transcripts and a statement of purpose with your application forms. Some programs may require a list of advanced mathematics courses with your application, while others administer placement examinations when you enroll in the graduate program, to test your knowledge of basic mathematical concepts, beyond what the GRE mathematics exam demonstrates.

Step 4: Choose a Track

Doctoral programs are often divided into a pure or theoretical track and an applied track, although significant overlap exists between them. If you choose the theoretical track, most schools require you to demonstrate competence in a core set of classes, which may include topology and geometry, algebra and analysis. In an applied track, you may take some of these core classes, but you might also take mathematics-related classes in another field like physics, economics, astronomy or another field of interest.

Whichever track you choose, your first two years are likely to spent attending classes, seminars an lectures by visiting mathematicians. Once the basic courses are completed in your first year, your program typically allows you to select mathematics courses of interest, including topology, combinatorics, functional analysis, homology and functional analysis. Toward the end of your second year or the beginning of your third, you'll probably be required to take a qualifying examination. This examination may be written, oral or a combination of the two, and your professors design the exam to test your knowledge of advanced mathematical concepts and theories.

Upon passing your qualifying examination, you'll select a dissertation topic and advisor. Your final three years are spent researching and writing this dissertation, allowing you to pursue independent scholarship that contributes to the study of mathematics. Depending on your track, your dissertation topic may discuss applying specific mathematical principles and theories to solving problems in other fields, for example, applying algebraic principles to biochemical reactions. Or, your dissertation might suggest new advances mathematical research like using number theory and algebraic equations to create new forms of cryptography.

Step 5: Find a Job

Upon completing your doctorate, you'll face keen competition for employment, although the U.S. Bureau of Labor Statistics (BLS) projected job growth from 2014-2024 of 21% for mathematicians, which was a faster growth than the average for that period ( Applied mathematicians were expected to have slightly better prospects than those in theoretical mathematics, since competition for tenure-track jobs in academia was strong and many industries are eager to apply mathematical principles to solving industry issues. According to the BLS in May 2014, 3,500 mathematicians were employed in the U.S.

Jobs in Theoretical Math

If you opt for theoretical training you most likely will find employment as a faculty member at a university, where you'll divide you time between teaching and research. Graduate students might assist with your teaching duties if you're assigned to teach undergraduates. You may conduct your research privately or in collaboration with one or more other mathematicians. The BLS reported in May 2015 that colleges, universities and professional schools employed 380 mathematicians. Average annual wages for university and college mathematicians were $65,610 in May 2015, according to the BLS.

Jobs in Applied Math

If you choose to study applied mathematics you have career options in finance and insurance, healthcare, information science, government, scientific research, business analysis and education. Possible job titles include biometrician, econometrician, psychometrician, cryptanalyst or biomathematician. In May 2014, the BLS reported that approximately 970 mathematicians worked for the federal executive branch and earned an average annual salary of $108,890 as of May 2015. Another 700 worked for scientific research services, earning an average annual salary of $133,750. Scientific and technical consulting services employed 200 mathematicians, who earned an average annual salary of $122,260.

What Are Some Related Alternative Careers?

Mathematicians have usually pursued a doctoral degree in either theoretical or applied mathematics and are therefore qualified for a number of other career paths. You could pursue a job as a statistician, which involves using math and statistics to solve problems in real-world industries. You may also be interested in a job as a survey researcher, which requires advanced math skills. These professionals design surveys which often include numerical data that must be analyzed. There are also a number of positions as financial analysts that mathematicians could qualify for.

To continue researching, browse degree options below for course curriculum, prerequisites and financial aid information. Or, learn more about the subject by reading the related articles below:

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