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.

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Projects

Side projects and math.

LeMMA: Learning Math by Meta-Adaptation

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.

XiaoPrompt

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

AgenTeX

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.

Derangements and Rubik's Cubes

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

Probabilistic Estimation of Prime Number Density

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

Articles

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.


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