Overview
Axioms is a mathematics learning platform built around mastery. It does not try to be a video library with exercises attached. It tries to take a scoped idea, generate representative problems for it, and keep the learner in that idea until they can do the work.
The problem
A lot of learning software confuses exposure with understanding. You watch, you click, you get a green tick, you move on. The course is complete and the idea is not. In mathematics that failure is expensive, because later ideas are built on earlier ones. I wanted software that would rather hold you in a concept than congratulate you for leaving it.
The idea
Mastery is the product. That means three things. Concepts have to be small enough to finish. Practice has to cover the actual idea, not one lucky example. And the system, not the learner's guilt, should be responsible for noticing when mastery is not there yet. Procedural generation exists to serve that: a fresh, valid problem so practice cannot collapse into memorising a worksheet.
Product / design decisions
The unit of progress is a concept, not a course week. Problems are generated against that concept rather than stored as a fixed quiz. Where AI appears, it is in service of the learning experience — helping with explanation and guidance — not as a chatbot bolted onto a PDF. The interface should feel closer to sitting with a problem than browsing a content catalogue.
Engineering
The product is a Next.js client with a Spring Boot API and PostgreSQL. Generated problems have to be valid, well-scoped and checkable, which is a harder engineering problem than rendering content. AI-assisted features sit on top of that structure rather than replacing it. The database holds the learning model: concepts, attempts, and whatever signals are used to decide that a learner is not done yet.
Challenges
Generating mathematics is easy to demo and hard to trust. A problem can look right and still teach the wrong idea, sit at the wrong difficulty, or be impossible to mark cleanly. Defining mastery without fake precision is the other difficulty. I do not want a percentage that pretends to be a mind. I want a model that is honest about coverage: have you seen the representative cases, and can you do them.
What I learned
Pedagogy is a product decision. If the concept map is wrong, no amount of interface polish will produce learning. I also learned that AI is useful here when it is constrained — as a way to explain, vary, or help — and unhelpful when it becomes the syllabus.
Current status
The product is live at axioms.co.za and still being shaped. I am not publishing learner counts or outcome statistics here.
Links
Repository links are on GitHub where the code is public. I am not publishing internal or employer code here.