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.
We are looking for a Research Intern to work at the intersection of formal methods, physics and AI. This role is particularly well suited to PhD students interested in pioneering the application of Lean4 to physics, bridging the gap between formal logic and the physical sciences while leveraging tools that make formal reasoning more scalable and useful in practice.
The internship will focus on high-value research directed towards enabling systematic use of formal methods for science. The intern will collaborate with the team in developing the formal infrastructure capable of supporting scientific applications of formal methods.
Your mission
- Design, develop and test the formalization of a targeted scientific subfield in collaboration with our team
- Explore, design and implement custom Lean4 tactics, metaprogramming or related tooling to automate the heavy lifting of physics formalization
- Conduct high-quality scientific work that can be published at top tier venues or contribute to major open source projects
- Currently pursuing a PhD (preferred), or advanced Master’s degree in Physics, Mathematics, Computer Science, Artificial Intelligence, or a related field
- Strong proficiency in Lean4 is required (1+ years, contribution to open-source projects)
- Background in one of the following:
- Formal methods / theorem proving
- Physics, Mathematics
- [nice to have] AI, especially in mathematically structured domains
- 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 Spain.
Relocation support:
For candidates relocating from another country, Axiomatic will cover temporary housing and travel to/from Barcelona 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
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
Duration:
3–6 months (typically starting between June and September, depending on candidate availability)
Successful interns may be considered for full-time roles following the internship.
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.
