About the Role

We build the fastest GPU compiler in the world. Most compilers have to preserve correctness at every transform, constraining how far they can search, while we prove correctness at the end instead, allowing us to search a far wider space, with agents, with RL, with anything that works and still guarantees the result. It's why we hold #1 on NVIDIA's own kernel benchmark across hundreds of production kernels.

Our core proof machinery is real and it works, but right now there are some rough edges that limit the number of kernels we can prove. With the rise of AI capabilities in mathematics combined with our bit-identical models and tools, such as our own model for large-scale Lean proof writing, things that were nearly impossible just a few months ago are now totally viable, but we need someone who figures out what theory we're missing, builds it and then coordinates with the engineering team to deploy it at scale, which is why we are hiring a Member of Mathematical Staff to own the math behind the proof engine and other surfaces for applying rigorous math to an increasingly wishy-washy domain.

This is not an advisory role and you'll have access to better tooling than anywhere else, such as bit-exact software models of hardware components like the tcgen05, a compiler capable of emitting code at a lower level than publicly possible, and frontier models with capabilities tailored to what your work needs, trained with our team.

What You'll Do

• You'll own the proof engine end-to-end, ensuring we can prove kernels across all edge cases
• You'll collaborate with the engineering team on building formal models of new hardware
• You'll work on formalizing numeric stability and what drives model convergence across diverse architectures
• You'll work on research around the extent to which we can predict training divergence during runs
• You'll collaborate with the research team on our post-training efforts around formal proofs and program verification
• You'll work on formalizing low-precision computation and its numerical stability
• You'll collaborate with the engineering team on formally proving sandboxes safe

What We're Looking For

• A PhD in Math is strongly recommended but not required: what matters is what you've proven and built
• Someone with good judgement about when a full proof is worth it and when a cheaper guarantee is enough
• Someone who's pragmatic about tooling and knows when SMT works, when an interactive proof is necessary and when custom decision procedures are necessary
• Someone who's comfortable owning an open-ended problem where you set the research agenda yourself
• Someone who can explain a proof strategy to an engineer who doesn't know the math, and push back when they want to cut corners

Nice to Have

• Someone who's contributed to projects such as Mathlib, Flocq or seL4.
• Someone with hands-on experience working with Lean or Rocq
• Someone who's done work or published in the field of program verification
• Someone who's done work or published in the field of numerical analysis or numerics
• Someone who's done work or published in the field of optimization theory or the dynamics of stochastic training
• Someone with deep knowledge in the field of floating-point formalization

Why Join Us

You will sit in the only place in the world right now working on guaranteeing the correctness and training stability of frontier models, which is one of the most important problems of our time, with the tools and freedom to actually solve it. The truth is that most formal methods work never leaves the paper and most ML work never gets near a proof. Here, the proof engine decides what is allowed to ship into production, so your work sits on the critical path of everything we do and gets tested against more kernels in a day than most verification tools see in their lifetime.

We invest heavily in AI tooling for mathematics, from our own model for large-scale Lean proof writing to bit-exact models of the hardware, so you spend your time on the theory and not the tedium, and get from idea to proof as fast as possible. Beyond that, the people who reverse-engineered the tensor cores, write the compiler and train the models you are proving and using for your mathematics are the same people you eat lunch with, so when a proof hinges on what the silicon actually does, the answer is a conversation away.

We're a small team operating at frontier scale. We pre-trained foundation models on 4,000 AMD GPUs as a team of three, designed and brought up GB300 NVL72 clusters and designed a TOP500 supercomputer.

We believe that hard problems get solved in person and most of our work happens at our office in San Francisco. We offer relocation assistance and, where possible, we'd like you here as often as possible.

The base salary range for this full-time position is $225,000-$315,000, plus meaningful equity and benefits.