Mathematics of Computing Research Intern - Summer 2026

Introduction Join IBM Research, where we prioritize innovation and the impact of technology in society. As a member of our team, you'll engage in cutting-edge research and development, working on projects that define the future of computing and technology. Your contributions will drive the creation of solutions that make a real difference for clients and communities. At IBM, we encompass a wide range of fields, including Research, Software, and Infrastructure, placing you at the forefront of growth and innovation. Your role and responsibilities In this role, you will: Develop innovative mathematically based methods and algorithms in areas such as numerical linear and multi-linear algebra, computational complexity theory, fully homomorphic encryption, optimization (with a focus on discrete optimization and reinforcement learning), algorithmic foundations of neural networks, and quantum-centric high-performance computing. Conduct research to formulate new mathematical and algorithmic frameworks that incorporate learning, optimization, and encryption within scalable computational systems. Implement advanced techniques, including AI model training, numerical and algebraic solver development, and quantum-classical computational methods. Engage in software prototyping across classical, distributed, and quantum systems. Validate your work through theoretical and practical benchmarks. Develop and demonstrate algorithms and systems that push the boundaries of AI in mathematics, secure computation, and scientific advancement. Required technical and professional expertise Strong background in numerical linear and multi-linear algebra. Experience with complexity theory, particularly related to meta-complexity and foundation models. Solid understanding of formal optimization methods. Knowledge of AI for algorithmic reasoning. Exposure to quantum-centric high-performance computing. Preferred technical and professional experience Familiarity with fully homomorphic encryption. Experience in probability theory and stochastic processes. Proficiency in algorithms, especially those involving neural networks. IBM is dedicated to fostering a diverse work environment and is an equal-opportunity employer. We welcome all qualified applicants to apply, regardless of race, color, religion, sex, gender identity or expression, sexual orientation, national origin, caste, genetics, pregnancy, disability, neurodivergence, age, veteran status, or any other characteristic. We also adhere to all fair employment practices regarding citizenship and immigration status.

Apply Now