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 As an Applied Researcher specializing in Formal Methods for Physics, you will join a focused team, playing a key role in building new formal verification tools for science and engineering. Your responsibilities will include assessing Lean4 code for formalization, writing specific Lean4 libraries, proof integrity, and overall code quality. You will also manage data curation, conduct benchmarking to evaluate performance, analyze reasoning flaws and propose solutions. Close collaboration with our dedicated cross-functional team - consisting of Lean experts, mathematicians, physicists, AI researchers and software engineers - will be essential to the success of the project.

The role is based in Barcelona, Spain.

Not based in Barcelona? No problem, we still encourage you to apply. Axiomatic is committed to hiring the best talent globally, and if you’re open to relocating, we’re open to discussing how we can support you. Your Mission

• Lean4 development: Build and maintain in-house Lean4 libraries, ensuring scalability, maintainability, and compatibility with our AI pipeline.
• Code Evaluation: Assess Lean4 code for formalization, proof correctness compared to scientific requirement, and overall code quality.
• Data & Benchmarking: Curate datasets, run benchmarks, and analyze performance results to guide improvements.
• Cross-Functional Collaboration: Work closely with our focused research team to ensure fast-paced progress.

Key Requirements

• Master’s degree in Mathematics, Physics, Computer Science, Artificial Intelligence or related field
• 1-2 years of experience, preferably in a mathematical, engineering, scientific, or academic setting
• Strong communication skills
• Ability to collaborate effectively within a multidisciplinary and multicultural environment
• Curiosity, and a proactive, solution-oriented mindset
• Excitement to work in a dynamic and fast-paced environment, ability to thrive in ambiguity.

Technical Skills

• Strong experience in applied formal methods and automated theorem proving
• Lean4 (1+ years at least)
• Understanding of maths and physics
• Programming skills, software design patterns

Preferred Qualifications (Nice To Have)

• Proven excellence in relevant areas (e.g., awards, competition wins)
• PhD in a scientific discipline (Physics, Mathematics, Machine Learning, etc.)
• Demonstrated curiosity and passion for AI (e.g., personal projects, outreach activities, hobby work)
• Proven ability to independently solve complex problems or lead challenging projects
• Understanding of AI and Machine Learning fundamentals
• Academic or practical background in physics or other natural sciences, authorship in related publications
• Strong proficiency in Python programming

What We Offer

• Competitive compensation
• Stock Options Plan: Empowering you to share in our success and growth.
• Cutting-Edge Tools: Access to state-of-the-art tools and collaborative opportunities with leading experts in artificial intelligence, physics, hardware and electronic design automation.
• Work-Life Balance: Flexible work arrangements in one of our offices with potential options for remote work.
• Professional Growth: Opportunities to attend industry conferences, present research findings, and engage with the global AI research community.
• Impact-Driven Culture: Join a passionate team focused on solving some of the most challenging problems at the intersection of AI and hardware.

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 x 30 mission. This is your opportunity to contribute to the development of new AI architectures that can reason coherently and produce interpretable and verifiable solutions. Consequently, see those ideas commercialized into products that will shape the future of hardware and computing, while collaborating with a global team of engineers and AI specialists. We believe in pushing the boundaries of what is possible and continuously seek to redefine the intersection of AI, with focus on formal consistency. If you're ready to take your expertise in artificial intelligence and physics to the next level, we want to hear from you!

We are primarily looking to hire in person in Barcelona, but we will also consider remote or hybrid options for this role.

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.