Mathematics of Computing Research Summer Intern : 2026

Introduction

IBM Research takes responsibility for technology and its role in society. Working in IBM Research means you'll join a team who invent what's next in computing, always choosing the big, urgent and mind-bending work that endures and shapes generations. Our passion for discovery, and excitement for defining the future of tech, is what builds our strong culture around solving problems for clients and seeing the real world impact that you can make.

IBM's product and technology landscape includes Research, Software, and Infrastructure. Entering this domain positions you at the heart of IBM, where growth and innovation thrive.

Your role and responsibilities

Develop new mathematically grounded methods and algorithms in one or more of the following areas : numerical linear and multi-linear algebra, computational and meta-complexity theory, fully homomorphic encryption, optimization (especially discrete optimization and reinforcement learning based methods), algorithmic foundations of neural networks, quantum-centric high-performance computing, probability theory and stochastic processes, and AI for algorithmic reasoning. The job requires research into new mathematical and algorithmic formulations that integrate learning, optimization, and encryption within scalable computational frameworks; implementation including AI model training, development of numerical and algebraic solvers, encrypted and quantum-classical computation, and advanced algorithmic techniques for neural and optimization-based architectures; computer programming and software prototyping across classical, distributed, and quantum systems; validation on theoretical and practical benchmarks; and development and demonstration of working algorithms and systems that advance the frontiers of AI for mathematics, secure computation, and scientific discovery.

Required technical and professional expertise

Numerical linear and multi-linear algebra

Complexity theory, particularly as related to meta-complexity and foundation models

Knowledge of formal optimization methods

AI for algorithmic reasoning

Quantum-centric high-performance computing

Preferred technical and professional experience

Fully homomorphic encryption

Probability theory and stochastic processes

Algorithms, particularly as related to neural networks

IBM is committed to creating a diverse environment and is proud to be an equal-opportunity employer. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, gender, gender identity or expression, sexual orientation, national origin, caste, genetics, pregnancy, disability, neurodivergence, age, veteran status, or other characteristics. IBM is also committed to compliance with all fair employment practices regarding citizenship and immigration status.