How to apply for Research Fellowship

About Theorem

Theorem is an AI company building systems for formal program verification. The goal is to improve the reliability of all software. The team includes engineers and researchers from cryptography, infrastructure, security research, and top-tier companies.

About the role

This is a 3–6 month research fellowship at a programming languages and AI lab. You will conduct research and develop products that let AI models perform software engineering tasks far beyond current human capabilities. The work targets problems orders of magnitude larger, faster, or harder than state-of-the-art, with a focus on last-mile technical challenges.

A typical day

You will spend time reading research, writing code, and testing ideas for scaling correctness feedback. You will collaborate with engineers and researchers on last-mile technical challenges. The work is remote and full-time, with a focus on problems larger and harder than current state-of-the-art.

Who Theorem is looking for

• Background in programming languages, formal verification, or AI/ML research.
• Experience building systems or products, not just writing papers.
• Comfort with solving last-mile technical challenges in complex codebases.
• Interest in scaling correctness feedback for AI software engineering.

Tips for this application

• Highlight any work on formal verification, program analysis, or programming languages.
• Describe specific projects where you solved hard technical problems at scale.
• Explain how your research connects to AI-driven software engineering.
• Mention why a 3–6 month fellowship fits your current stage.
• Reference Theorem's focus on formal program verification and correctness feedback.

What to cover in your cover letter

Emphasize your experience with formal methods or programming languages. Explain how you have built systems that scale. Connect your research interests to AI software engineering. State why a short-term fellowship at Theorem is the right next step.

Research before applying

• Read Theorem's published research or product pages on formal program verification.
• Look up the backgrounds of the team in cryptography, infrastructure, and security.
• Understand the current limits of AI models in software engineering tasks.
• Check what 'correctness feedback at arbitrary complexity' means in practice for their products.

Likely interview topics

Based on the job description, expect questions about:

• How formal verification can be applied to AI-generated code.
• Your approach to solving last-mile technical challenges in large systems.
• Trade-offs between scalability and correctness in program analysis.
• Experience with programming languages, type systems, or verification tools.
• How you would design a product to scale correctness feedback for AI software engineering.

Common mistakes to avoid

• Applying without any background in programming languages or formal verification.
• Focusing only on AI/ML without connecting to software correctness.
• Treating the fellowship as a generic internship rather than a research role.