Nick Rui

I'm an undergraduate at Stanford University studying math and computer science. I'll be interning at Databricks this summer as a Kleiner Perkins Engineering Fellow. Previously, I interned at Amazon Web Services and worked in outdoor swimming pool management and operations.

Projects

Side projects and math.

Meta-adaptation framework for theorem-proving LLMs to self-synthesize domain-specific data at inference time.

Vital Cue

Voice and AI-powered platform for patient care documentation. Built for EMS.
Acquired by First Due.

Agentic inference optimization with dynamic speculative decoding and GPU orchestration.
Winner at TreeHacks.

Prompt distillation and translation API to optimize token efficiency.
Winner at HackMIT.

Cursor for LaTeX.
Winner at AgentOps x Stanford Hackathon.

Bertrand's Postulate

A proof there is always a prime between n and 2n. Bored on an airplane.

Highlighting Burnside's lemma and applications to group derangements and Rubik's cubes.

Constructing a Bayesian primality test building on ideas from Fermat's Little Theorem.

I write about math on Substack.

An 'Odd' Application of Linear Algebra
December 2025

The oddtown theorem.

Balls (in 10+ dimensions)
August 2025

A weird fact about ten dimensional balls.

Template from Jon Barron.