Mathematics, computing & theater

Will Gao.

I’m a fourth-year in the University of Washington’s computer science BS/MS program, also majoring in pure mathematics.

This summer I was an applied scientist intern at Madrona Venture Group, where I worked on large-scale data and ML problems and designed a founder-discovery model for the firm’s investors. My interests were previously in combinatorial optimization and probability; I’m now shifting toward empirical AI. I also write about musical theater.

I’m looking for a model-focused machine learning engineering role at a startup, or a research residency, for June 2027–June 2028, before returning to UW for the master’s year.

Selected projects

Formal verification · Experimental

Lale

Your proof, checked step by step in Lean.

Maps the definitions, lemmas and theorems in an Overleaf paper, restates each step of a written proof in Lean 4, and shows exactly which step fails. It checks whether the proof works, not just whether the result is true. A Chrome extension and macOS app; Lean and Mathlib run locally.

Research & teaching

Ongoing
Not yet published

Ising formulations for combinatorial optimization

Ising formulations for the traveling salesperson problem and related graph optimization problems. Mentored by Prof. Jerry Li (UW), collaborating with Medha Mittal (UW) and Devrath Iyer (Stanford), with guidance from Prof. Sara Achour (Stanford).

Writing

All writing

Extended lecture notes

All 7 notes

I sometimes expand lecture notes into a more systematic treatment, filling in proofs and connecting ideas. Here are a few of those notes.

September 2026

Reinforcement Learning I

Why does an optimal policy exist, and how can we find it? A fixed-point argument for finite discounted Markov decision processes leads to value iteration and policy iteration.

December 2025

From Martingales to Diffusion Generators

How can we describe when and where a diffusion leaves a region? Starting with conditional expectation and Itô calculus, these notes connect stochastic paths to boundary-value problems.