Post Header Header image by gabrielzschmitz, licensed under Creative Commons 4.0 Attribution license.


Mathematics is an interconnected web of concepts, theorems, and proofs, each building upon others in intricate ways. But what if there were a structured, searchable way to navigate this vast landscape? That’s the idea behind my latest project: Axiom Nexus, or for short, AxioN.

The Vision

The goal is to create an online resource where users can:

  • Search for mathematical concepts, theorems, definitions, and proofs.
  • View relationships between topics using tags to get that distances.
  • Export expressions and code in multiple formats (e.g., LaTeX, Unicode, etc).
  • Get good references and explanations.

In essence, this platform aims to be more than just a collection of definitions – it should serve as a dynamic tool for understanding mathematical structures and relationships.

The Name Choice: Axiom Nexus (AxioN)

An axiom is a fundamental truth upon which mathematical structures are built. A nexus is a hub of connections, linking different entities together. Combining these ideas, Axiom Nexus (AxioN) represents a centralized hub for mathematical knowledge, where foundational truths interconnect with theorems, definitions, and proofs. The short form, AxioN, cleverly echoes the idea of axioms while maintaining a sleek and memorable identity.

Technical Choices

To ensure simplicity, scalability, and usability, I’ve chosen a carefully designed stack that aims to balance efficiency with ease of use:

Backend: Golang

Golang is a fast, compiled language that excels at handling concurrent tasks efficiently. By using Golang for the backend, the system can handle multiple requests seamlessly, ensuring a smooth user experience even as the database grows. Its robust standard library and simplicity in deployment should make it a great choice for the project.

Frontend: HTMX

Instead of using a complex frontend framework, I opted for HTMX, a lightweight JavaScript alternative that allows for dynamic content updates without the need for a full-page reload. This keeps the interface responsive and interactive while maintaining simplicity. HTMX enables features like infinite scrolling, inline content updates, and lazy loading, all without writing large amounts of JavaScript.

Database: PostgreSQL

To handle structured mathematical data efficiently, PostgreSQL serves as the primary database. It offers:

  • Scalability: Handles large datasets with ease.
  • Complex Queries: Ideal for linking mathematical concepts and exploring relationships through graph-like structures.
  • ACID Compliance: Ensures reliability and consistency in stored data.

With PostgreSQL, the system can efficiently manage theorem dependencies, search queries, and user contributions.

Data Format: YAML Files

Each mathematical concept, theorem, or proof is described using YAML files. This choice was made to prioritize readability and ease of contribution. YAML is human-friendly and allows for:

  • Structured data representation without excessive complexity.
  • Simple version control, making it easy to track changes and updates.
  • User contributions, as anyone can edit or add new mathematical entries without needing database access.

Code Rendering: highlight.js

For examples that involve programming or pseudo-code, highlight.js ensures proper syntax highlighting. Whether it’s Python, C++, or LaTeX-formatted proofs, this makes code snippets easy to read and understand.

Mathematical Notation: MathJax

Since mathematics relies heavily on proper notation, MathJax is used for rendering LaTeX equations. This ensures:

  • High-quality mathematical typography, making proofs and equations clear.
  • Browser compatibility, so users can view complex formulas without additional software.
  • Support for interactive content, allowing users to copy and manipulate formulas directly from the interface.

Current Status

Right now, the project is in its early stages. I’m focusing on:

  • Structuring the database to store mathematical information efficiently.
  • Designing an intuitive search mechanism to help users find what they need.
  • Implementing tagging and connections so that related ideas naturally link together.

Why This Matters

Many existing resources present mathematics in a linear, textbook-like format. But real mathematical thinking isn’t linear – it’s a web of interconnected ideas. By structuring knowledge in a way that mirrors how mathematicians think, this project could help students and researchers explore mathematics more intuitively.

This is just the beginning, and I’m excited to see where this journey leads. If you have ideas or want to contribute, stay tuned for updates!


- gabrielzschmitz