Mathematicians use advanced mathematics to develop and understand mathematical principles, analyse data, and solve real-world problems.
Mathematicians typically do the following:
- Expand knowledge in mathematical areas, such as algebra or geometry, by developing new rules, theories, and concepts
- Use mathematical formulas and models to prove or disprove theories
- Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, or other fields
- Develop mathematical or statistical models to analyse data
- Interpret data and report conclusions from their analyses
- Use data analysis to support and improve business decisions
- Read professional journals, talk with other mathematicians, and attend professional conferences to maintain knowledge of current trends
Applied mathematicians use theories and techniques, such as mathematical modeling, to solve practical problems. These mathematicians typically work with individuals in other occupations to solve these problems. For example, they may work with chemists and materials scientists and chemical engineers to analyse the effectiveness of new drugs. Other applied mathematicians may work with industrial designers to study the aerodynamic characteristics of new automobiles.
Theoretical mathematicians do research to identify unexplained issues in mathematics and resolve them. They are primarily concerned with exploring new areas and relationships of mathematical theories to increase knowledge and understanding about the field. Although some may not consider the practical use of their findings, the knowledge they develop can be an important part of many scientific and engineering achievements. Despite the differences, these areas of mathematics frequently overlap.
Many mathematicians will use both applied and theoretical knowledge in their job duties. However, most people with a degree in mathematics or who develop mathematical theories and models are not formally known as mathematicians. Instead, they work in related fields and professions. In the computer systems design and related services industries, they may be known as computer programmers or systems analysts. In finance, they may be known as quantitative analysts, financial analysts, or statisticians. Computer and information research scientists, physicists and astronomers, economists, actuaries, operations research analysts, and many other occupations also use mathematics extensively. Some people with a mathematics background become high school mathematics teachers. Many people with a PhD. in mathematics, particularly theoretical mathematics, work as lecturers in universities. They usually have a mix of teaching and research responsibilities. Some may do individual research or collaborate with other professors or mathematicians. Collaborators may work together at the same institution or from different locations.