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Research Internship in Formal Methods for Science

Axiomatic AIBoston, US / Toronto, Canada / Castelldefels (Barcelona), Spain
On-site Internship

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Experience Level

Entry Level

Qualifications

Key RequirementsCurrently enrolled in a PhD program (preferred) or advanced Master’s degree in Computer Science, Artificial Intelligence, Mathematics, Physics, or a related discipline. Strong proficiency in Python is essential. A background in one of the following areas:AI / machine learning (agentic AI, knowledge retrieval, graphs, LLMs, deep learning, etc.)AI applications in science, particularly in physics and other mathematically rigorous domains. Research Engineering or Software Engineering.

About the job

About Axiomatic AI

Axiomatic AI develops AI systems that combine deep learning, formal logic, and physics-based modeling. The goal: create verifiable, interpretable AI that supports human researchers in scientific and engineering fields. The company’s 30×30 mission targets a 30-fold increase in the speed, accessibility, and affordability of semiconductor and photonic hardware development by 2030.

With teams in Boston, Toronto, and Castelldefels (Barcelona), Axiomatic AI is working to transform hardware design and simulation, moving ideas from research to commercial products.

Research Internship Overview

This internship centers on formal methods, artificial intelligence, and scientific reasoning. It’s especially suited for PhD candidates interested in advancing AI’s role in science and engineering, and in building tools to validate scientific results. The work focuses on automated verification of scientific reasoning, contributing to the design of AI agents that handle complex mathematical formalization, knowledge retrieval, and both formal and informal verification methods.

What You Will Do

  • Develop tools for formal reasoning, such as improved library search, theorem retrieval, and formalization assistants.
  • Explore Lean metaprogramming or similar formal methods tools for research applications.
  • Design verification pipelines for complex equation derivations, helping connect AI systems with physics.
  • Work closely with researchers to define a focused project that advances Axiomatic AI’s capabilities and contributes to scientific understanding.
  • Carry out research with the potential for publication at venues like ICLR, ICML, or NeurIPS, or contribute to major open-source projects.

Locations

  • Boston, US
  • Toronto, Canada
  • Castelldefels (Barcelona), Spain

About Axiomatic AI

Axiomatic AI is pioneering a new era of AI systems that emphasize rigorous scientific methods. Our innovative approach combines advanced AI techniques with foundational principles of formal logic and physics, creating powerful tools that enhance research capabilities in science and engineering. Join us as we strive to revolutionize hardware development and simulation.

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