Navigating Competition
The occupation is small, and there are relatively few Theoretical Mathematician positions. With a background in advanced mathematical techniques and modeling, many candidates can navigate the strong competition and find positions in other closely related fields.
In addition to working with integers, Theoretical Mathematicians deal with abstract structures such as rings in the algebraic number theory. Applying theories to shapes and geometry is an example of how a particular skill can enhance effectiveness in this field.
Teaching
With a Mathematics background, you may choose to teach the subject at middle or high school. Many people with a PhD in Mathematics, particularly Theoretical Mathematics, work as postsecondary teachers, usually combining teaching and research responsibilities. They may conduct individual research or collaborate with other professors and Mathematicians. Collaborators may work together at the same institution or work from different locations.
Research
As a Theoretical Mathematician, you would conduct research to identify unexplained issues in Mathematics and resolve them. You would be primarily concerned with exploring new areas and relationships of mathematical theories to increase knowledge and understanding about the field. Although the practical use of Theoretical Mathematicians’ findings seems limited, the experience they develop through research can be an essential component of many scientific and engineering achievements.
Applied Mathematics
When a Theoretical Mathematician combines Pure Mathematics with another specialty, such as flight engineering or medicine, they enter the field of Applied Mathematics. The typical work environment is either a research lab, often within a university or the private sector, or a regular office setting.
Applied Mathematicians use theories and techniques such as mathematical modeling to solve practical problems, often working with individuals in other occupations. For example, they may work with chemists, materials scientists, and chemical engineers to analyze the effectiveness of new drugs. Other Applied Mathematicians may work with industrial designers to study the aerodynamic characteristics of new automobiles.
An Overlap Between Theory and Application
The fields of Theoretical and Applied Mathematics frequently overlap despite their differences, particularly as many Mathematicians tend to use knowledge from both areas to fulfill their job responsibilities.
Designations
Even with a degree in mathematics and despite developing mathematical theories and models, people may not be designated as Theoretical Mathematicians if they work in fields such as computer systems design. They may then be called computer programmers or systems analysts. Those working in finance may be known as quantitative analysts, financial analysts, or statisticians.
Utility Value
Computer and information research scientists, physicists and astronomers, economists, actuaries, operations research analysts, and many other occupations also use mathematics extensively.