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Internship – Research Intern (Formal Methods for Science)

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

About us

Axiomatic AI is building a new class of AI systems designed to reason with the rigor of the scientific method. By combining deep learning with formal logic and physics-based modeling, we create verifiable, interpretable AI systems that collaborate with and support human researchers in high-stakes scientific and engineering workflows. 

Our mission, 30×30, is to deliver a 30× improvement in the speed, accessibility, and cost of semiconductor and photonic hardware development by 2030. 

We aim to revolutionize hardware design and simulation in these industries and are building a team of highly motivated professionals to bring these innovations from research into commercial products.

Position overview

We are looking for a Research Intern to work at the intersection of formal methods, AI, and scientific reasoning. This role is particularly well suited to PhD students interested in advancing AI for science and engineering and building tools that enable verification of scientific output.

Specifically, the internship focuses on pioneering research on automated verification of scientific reasoning, such as architecting AI agents capable of navigating complex mathematical formalization workflows, knowledge retrieval systems, and formal and informal verification.


Your mission

  • Contribute to tooling for formal reasoning, such as improved library search, theorem retrieval systems, formalization assistants
  • Explore applications of Lean metaprogramming or related formal methods tooling
  • Architect verification pipelines for complex equation derivations, building the foundation where AI and physics intersect
  • Work closely with researchers to identify a tractable, meaningful project that advances both internal capability and research understanding
  • Conduct high-quality scientific work that can be published at top tier venues (ICLR, ICML, NeurIPS, etc.) or contribute to major open source projects

Key requirements

  • Currently pursuing a PhD (preferred), or advanced Master’s degree in Computer Science, Artificial Intelligence, Mathematics, Physics, or a related field
  • Strong proficiency in Python is required
  • Background in one of the following:
    • AI / machine learning (agentic AI, knowledge retrieval, graphs, LLMs, deep learning, etc.)
    • AI for science, especially in physics and other mathematically structured domains
    • Research Engineering / Software Engineering
  • Strong research skills and ability to work on open-ended technical problems
  • Strong analytical and communication skills
  • Ability to work independently while collaborating closely with researchers and engineers
  • Comfort working in a dynamic, fast-paced setting, thrives in ambiguity

Work model & location expectations

Work model:
On-site. Candidates are expected to be based at our Barcelona office.

Office location:
Carrer d'Esteve Terradas, 1
08860 Castelldefels, Barcelona, Spain

Our office is located in the Mediterranean Technology Park, within a university campus environment—just 20 minutes by train from central Barcelona and a 15-minute walk from the beach.

Work authorization:
Candidates must have (or be able to obtain) work authorization in one of our office locations.

Relocation support:
Axiomatic will support relocation by covering temporary housing and travel to/from the office location during the transition period.

Hiring manager & interview process

The interview process consists of four stages:

  • Culture interview
  • Technical + Hiring Manager interview (1 hour)
  • Team interview
  • Offer stage

Internship details

You will work directly with and be mentored by a global team of multidisciplinary experts pushing the boundaries of AI-assisted physics formalization.

Type:
Paid internship

Duration:
3–6 months (typically starting between June and September, depending on candidate availability)

Future opportunities:
Successful interns may be considered for full-time roles following the internship.

 


Why join us?

At Axiomatic AI, you will be working on technology that drives innovation in AI for scientific and engineering applications in line with our 30×30 mission.

This is your opportunity to contribute to the development of new AI methodologies that improve scientific modeling, reasoning, and design. You will work on research questions with both theoretical depth and practical relevance, while collaborating with a global team of engineers, scientists, and AI specialists.

We believe in pushing the boundaries of what is possible and continuously seek to redefine the intersection of AI, uncertainty-aware modeling, and scientific computation. If you're excited by technically demanding research and want to help shape the future of AI for engineering and hardware, we want to hear from you.

Worried about not meeting every qualification? Studies show that women and people of color are less likely to apply for jobs unless they meet every listed requirement. At Axiomatic AI, we are dedicated to creating a diverse, inclusive, and authentic workplace. If this role excites you but your background doesn’t perfectly match every qualification, we still encourage you to apply. You could be the perfect fit for this position or another opportunity with us.



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