About The Lumenary

Our mission

The Lumenary exists to make rigorous, joyful and intellectually liberating mathematics education available to people everywhere — for free, in their own languages, without accounts, advertising or paid subscriptions.

Our first subject is Lumenary Math: a curriculum that will run from counting in kindergarten to the first year of graduate school, with optional pathways into research. We are at the very beginning. Five lessons and seven Wonder Trails exist today; the rest of the curriculum is mapped but not yet written. We would rather build a small thing that is trustworthy than a large thing that is not.

One mathematics. Many languages. Every nation.

Christian inspiration — offered, never imposed

The Lumenary is inspired by historic Christian values. We say so openly, because transparency is one of them. These values shape how we build and how we treat learners:

• Truthfulness — we never claim a proof, test, review or translation that has not happened.
• Wisdom and humility — we label uncertainty, admit our limitations, and welcome correction.
• Love of neighbour and human dignity — every learner, everywhere, deserves patient, respectful teaching. We never use shame, manipulative streaks or public rankings.
• Generosity — everything is free and openly licensed.
• Stewardship — the site is light, works on inexpensive devices, and is cheap to host.
• Intellectual honesty — mathematical statements are justified mathematically, never by authority.
• Wonder at creation — mathematics is beautiful, and curiosity is worth cultivating for its own sake.
• Service — the project exists for its learners, not the other way round.

Christian inspiration is never a prerequisite. You do not need to share any belief to learn here, and nothing in the mathematics depends on one. A few lessons contain short, clearly marked optional reflections; they are collapsed by default, separate from the mathematical instruction, and can simply be skipped.

We represent mathematicians and mathematical traditions of every religious and non-religious background accurately and respectfully. Truth is not determined by the identity of the person who discovers it.

How we teach

Every suitable idea is explored in three complementary modes:

• Human — intuition, examples, pictures, conjectures and clear human proofs.
• Formal — precise definitions and machine-checked proofs in Lean 4.
• Computational — Python experiments that run in your browser, with honest labels for what kind of evidence a computation provides.

The modes reinforce one another rather than living in separate books. Three optional feline narrators — Chloe the Mathematician, Margaret the Computationalist and Gideon the Formalist — appear now and then to ask the questions each mode cares about.

Our guiding principle is: Master the present. Glimpse the future. Never require the future to understand the present. Optional Wonder Trails invite curious learners to glimpse where an idea leads — towards groups, quotients, infinity or category theory — without ever counting against anyone who doesn't follow them.

Foundations: sets and categories

Earlier mathematics is built on sets. Higher mathematics increasingly speaks the structural language of categories. The Lumenary teaches both, from intuitive precursors in primary school to their rigorous forms at university — and it is careful about how they relate, without pretending they are interchangeable.

Academic integrity

The Lumenary aims to be more trustworthy than ordinary AI-generated material:

• A lesson is labelled formally verified only when every Lean declaration it cites appears in the latest build report, compiled, and does not depend on sorry. Each proof lists the axioms it uses, and we distinguish proofs that apply an existing library theorem from those proved here.
• An experiment is labelled computationally tested only when it ran and its automated tests passed.
• No content has yet been reviewed by a human mathematician, educator or translator. Every lesson says so. Agreement between AI systems is not treated as evidence of correctness.
• Translations other than English are machine-generated drafts and are labelled as such.

Built with AI, honestly

Much of the initial content and code was drafted with the help of AI systems. AI is a collaborator, not an oracle: the Lean proofs were checked by Lean, the Python experiments were run and tested, and everything else awaits human review. We will teach learners to use AI the same way — to ask good questions, critique arguments, find counterexamples and verify claims, rather than to depend on it.

Open source

• Software is licensed under Apache-2.0.
• Educational content is licensed under Creative Commons Attribution-ShareAlike 4.0 (CC BY-SA 4.0).
• Lean proofs and Python experiments are code, and so are Apache-2.0.

The Lumenary is an independent project. It is not affiliated with, or endorsed by, any university, school system, church or other institution.