Matthew McWilliams

Hello there!

My name is Matthew McWilliams.

I'm a dreamer.

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

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 →

LemmaCraft

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.