**Introduction** IBM Research provides an atmosphere in which basic research is combined with work on practical applications. Our permanent members, academic visitors, and post-doctoral fellows pursue research in pure and applied mathematics and in theoretical and exploratory computer science. **Your role and responsibilities** The fellowship provides scientists of outstanding ability an opportunity to advance their scholarship as resident department members at one of the IBM Research laboratories. The main hub of mathematical sciences activities in IBM Research is at the IBMThomas J. Watson Research Center in Westchester County, less than an hour north of New York City. Mathematical sciences research is also pursued at many of our global lab locations around the world. Close interaction with permanent department members is expected and encouraged, but fellows are free to pursue their own research interests. **Required technical and professional expertise** Doctoral-level expertise in one or more core fields of research includeing algorithms, applied probability, complexity theory, dynamical systems, numerical analysis and scientific computing, operations research, optimization and statistics. **Preferred technical and professional experience** Doctoral-level expertise in one or areas of particular interest including algorithmic game theory, artificial general intelligence, automated theorem proving and program synthesis, bioinspired information processing, theory and analysis of foundation models and machine learning, and algebraic/geometric data analysis.