Mathematics of Computing Research Summer Intern: 2026

Job Description:

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 education
Bachelor's Degree

Preferred education
Master's Degree

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