Mathematicians create, investigate and analyze mathematical structures in order to solve and understand mathematical problems. Mathematical structures are also found in related fields such as physics, computer science or economics.
Mathematicians work either as theoretical (pure) or as applied mathematicians. Both types of mathematicians develop new mathematical theories, techniques and approaches to solve problems.
Pure Mathematics demands abstract thinking for the development of mathematical theories and methods. These mathematical theories and methods are essential in the qualitative and quantitative description of our world and are practically applied in most sciences. It will, for example, be used to determine, all factors considered, how an industry must be managed in order to show maximum profit.
Applied Mathematics involves mathematical modelling, numerical analyses and operational research. It forms a bridge between Mathematics theory and practice and concentrates on solving problems in Engineering, Physics and Information Technology, as well as practical problems such as industrial research, research on population growth, the development of ecological systems and predictions on the performance of, for example, artificial limbs. Statistics and Information Technology are related fields of study.
Problems for which mathematical analyses are used to find solutions or to solve problems are in such areas as: medical research, agricultural research, psychological research, genetic research, engineering and ecological research. Mathematical models are also used in trade and industry, for example, in marketing management, quality control and auditing.
Most mathematicians work indoors in classrooms, offices and laboratories. The type, size, location and financial resources of the employer and the experience, education and ability of the mathematician determine the actual work setting.