Back to jobs

Internship – Research Intern (Formal Methods for Science)

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, 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

Key requirements

  • 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 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 team lead listed above will be the hiring manager.

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.



Apply for this job

*

indicates a required field

Resume/CV

Accepted file types: pdf, doc, docx, txt, rtf

Cover Letter

Accepted file types: pdf, doc, docx, txt, rtf

Select...
Select...
What is your availability for the internship? *
Select...

Voluntary Self-Identification

For government reporting purposes, we ask candidates to respond to the below self-identification survey. Completion of the form is entirely voluntary. Whatever your decision, it will not be considered in the hiring process or thereafter. Any information that you do provide will be recorded and maintained in a confidential file.

As set forth in Axiomatic_AI’s Equal Employment Opportunity policy, we do not discriminate on the basis of any protected group status under any applicable law.

Select...
Select...
Race & Ethnicity Definitions

If you believe you belong to any of the categories of protected veterans listed below, please indicate by making the appropriate selection. As a government contractor subject to the Vietnam Era Veterans Readjustment Assistance Act (VEVRAA), we request this information in order to measure the effectiveness of the outreach and positive recruitment efforts we undertake pursuant to VEVRAA. Classification of protected categories is as follows:

A "disabled veteran" is one of the following: a veteran of the U.S. military, ground, naval or air service who is entitled to compensation (or who but for the receipt of military retired pay would be entitled to compensation) under laws administered by the Secretary of Veterans Affairs; or a person who was discharged or released from active duty because of a service-connected disability.

A "recently separated veteran" means any veteran during the three-year period beginning on the date of such veteran's discharge or release from active duty in the U.S. military, ground, naval, or air service.

An "active duty wartime or campaign badge veteran" means a veteran who served on active duty in the U.S. military, ground, naval or air service during a war, or in a campaign or expedition for which a campaign badge has been authorized under the laws administered by the Department of Defense.

An "Armed forces service medal veteran" means a veteran who, while serving on active duty in the U.S. military, ground, naval or air service, participated in a United States military operation for which an Armed Forces service medal was awarded pursuant to Executive Order 12985.

Select...

Voluntary Self-Identification of Disability

Form CC-305
Page 1 of 1
OMB Control Number 1250-0005
Expires 04/30/2026

Why are you being asked to complete this form?

We are a federal contractor or subcontractor. The law requires us to provide equal employment opportunity to qualified people with disabilities. We have a goal of having at least 7% of our workers as people with disabilities. The law says we must measure our progress towards this goal. To do this, we must ask applicants and employees if they have a disability or have ever had one. People can become disabled, so we need to ask this question at least every five years.

Completing this form is voluntary, and we hope that you will choose to do so. Your answer is confidential. No one who makes hiring decisions will see it. Your decision to complete the form and your answer will not harm you in any way. If you want to learn more about the law or this form, visit the U.S. Department of Labor’s Office of Federal Contract Compliance Programs (OFCCP) website at www.dol.gov/ofccp.

How do you know if you have a disability?

A disability is a condition that substantially limits one or more of your “major life activities.” If you have or have ever had such a condition, you are a person with a disability. Disabilities include, but are not limited to:

  • Alcohol or other substance use disorder (not currently using drugs illegally)
  • Autoimmune disorder, for example, lupus, fibromyalgia, rheumatoid arthritis, HIV/AIDS
  • Blind or low vision
  • Cancer (past or present)
  • Cardiovascular or heart disease
  • Celiac disease
  • Cerebral palsy
  • Deaf or serious difficulty hearing
  • Diabetes
  • Disfigurement, for example, disfigurement caused by burns, wounds, accidents, or congenital disorders
  • Epilepsy or other seizure disorder
  • Gastrointestinal disorders, for example, Crohn's Disease, irritable bowel syndrome
  • Intellectual or developmental disability
  • Mental health conditions, for example, depression, bipolar disorder, anxiety disorder, schizophrenia, PTSD
  • Missing limbs or partially missing limbs
  • Mobility impairment, benefiting from the use of a wheelchair, scooter, walker, leg brace(s) and/or other supports
  • Nervous system condition, for example, migraine headaches, Parkinson’s disease, multiple sclerosis (MS)
  • Neurodivergence, for example, attention-deficit/hyperactivity disorder (ADHD), autism spectrum disorder, dyslexia, dyspraxia, other learning disabilities
  • Partial or complete paralysis (any cause)
  • Pulmonary or respiratory conditions, for example, tuberculosis, asthma, emphysema
  • Short stature (dwarfism)
  • Traumatic brain injury
Select...

PUBLIC BURDEN STATEMENT: According to the Paperwork Reduction Act of 1995 no persons are required to respond to a collection of information unless such collection displays a valid OMB control number. This survey should take about 5 minutes to complete.