Matt McWilliams

Projects and Blog

Hello there!

My name is Matt McWilliams.

I'm a dreamer.

I'm also a programmer, designer, reader, writer, tinkerer, builder, student, teacher, athlete, thinker, truth-seeker, and friend.


Projects and Writing

ACT Course
Education
Course
October 2026

My ACT prep course, still in very early development.

Guidance Scale Effects
AI
Writeup
December 2025

This project seeks to understand the effects of guidance scale on classifier-free sampling of conditional diffusion models. We trained a conditioned UNET diffusion model on the MNIST dataset and sampled using classifier-free guidance. Classifier-free guidance is essential for modern image generation diffusion models, allowing label-dependent features become more prominant simply by changing a variable, the guidance scale.

LemmaCraft
Math
Writeup
December 2025

LemmaCraft is a visual math proof engine with a custom parser and internal mathematical model. It allows its users to derive Peano-arithmetic results from only a few axioms. It consists of four chapters designed to teach users the software and introduce key lemmas: a tutorial chapter followed by three chapters that each cover a new mathematical domain: addition, multiplication, and exponentiation. In each chapter, players prove progressively more challenging lemmas about basic operations.

LemmaCraft

LemmaCraft is a math proof game in which you solve engaging math puzzles as you rebuild mathematics from the Peano axioms.

It also has a "story mode" if you'd like to solve math while participating in a cozy fantasy adventure.

Try it out →