From Chaos to Clarity: A Mathematical Approach To Maintainable and Performant React Application

React applications often suffer from increasing complexity, poor modularity, and unpredictable performance. Traditional code reviews and best practices can be subjective, leading to inconsistent results. But what if we could measure and optimize our architecture using mathematical foundations?

In this talk, we will explore:

• Graph Theory: How to model a React project as a graph, detect cycles, high-dependency files, and structural inefficiencies, and use modularity algorithms to guide refactoring.
• Category Theory: How composition, purity, and morphisms ensure predictable behavior and maintainable code through functors, monads, pattern matching, and optics.
• Lambda Calculus: How currying, lazy evaluation, memoization, and function composition optimize rendering performance and state transitions.

This talk bridges mathematics and software engineering to provide deterministic, structured solutions to common frontend challenges. By focusing on objective architectural analysis, composability, and performance optimizations, we can move beyond intuition and measure real software quality.