Research in MATH+ is multifaceted and comprises project-oriented, and project-independent mathematics research. The project-oriented research in MATH+ is structured into Application Areas (AA), Emerging Fields (EF), and Transfer Units (TrU), and focuses on application-oriented mathematics. On the other hand, the research activities in the eight mathematical research areas in MATH+ are not restricted to the classical form of a project and aim at the progression in mathematics itself.

The MATH+ Application Areas are tailored toward mathematical research in interdisciplinary application fields. They support cross-institution research projects that involve mathematicians as well as leading experts of the respective field of application. With the beginning of 2019, the following four Application Areas have taken up their activity:

- Life Science
- Materials, Light, Devices
- Networks
- Energy and Markets

The Emerging Fields are devoted to pioneering interdisciplinary research in new fields including the social sciences and humanities. Since January 2019, research activities in the following five Emerging Fields started:

- Extracting Dynamical Laws from Complex Data
- Digital Shapes
- Model-Based Imaging
- Particles and Agents
- Concepts of Change in Historical Processes

Transfer Units are designed for translational research with industry. Further details can be found here.

The present mathematical research areas are:

- Differential geometry, global analysis, and mathematical physics
- Algebraic and arithmetic geometry, number theory
- Stochastics and mathematical finance
- Discrete mathematics and optimization
- Geometry, topology, and visualization
- Numerical analysis and scientific computing
- Applied analysis and differential equations
- Mathematics of data science

MATH+ Transition Projects enable the transfer of promising research topics, e.g. from the Einstein Center for Mathematics ECMath, into the new context of MATH+. Transition Projects are short-term projects with the primary aim of re-bundling research activities and possibly integrating them into the MATH+ research agenda.