Research mathematicians work in a wide range of areas and carry out many different tasks. Common employers include private or government research laboratories, commercial manufacturing companies and universities.
The work often involves: proving deep and abstract theorems; developing mathematical descriptions (mathematical models) to explain or predict real phenomena such as the spread of cancer or the flow of liquids; and applying mathematical principles to identify trends in data sets. Applied research can also contribute to the development of a commercial product or develop intelligence about business trends.
Collaboration with other scientists and people in other commercial functions in industry is very common because the application of mathematics is so varied. Research is undertaken into a diverse range of pure and applied maths including algebra, analysis, combinatorics, differential equations, dynamic systems, geometry and topology, fluid mechanics, mathematical biology and numerical analysis.
Mathematicians in commercial organisations are involved in developing new products and providing insight into business performance. They are likely to be allocated specific projects. In smaller organisations, they may be involved in all stages of the product - from concept to customer.
In academic and research organisations, projects are undertaken to develop the understanding of particular areas of maths. There are very few pure research posts in universities, and most mathematicians working in research will also have teaching responsibilities. This may involve giving lectures to large groups of students, giving tutorials to small groups and setting and marking work including examinations.
Work in both settings usually involves some office-based activities and the use of specialist computer systems.
Tasks will vary depending on the specific work environment and organisation but may include the following:
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