About this library

Alphabeta Math is a library of 3,431 definitions, theorems, proofs, examples and counterexamples across 208 pages. Every proof is written in one format: numbered steps, each ending in a bracketed note naming exactly what it follows from — an earlier step, a stated assumption, or a named result elsewhere in the library. Dependencies are declared in machine-readable form, so the whole corpus is one acyclic graph you can walk in either direction.

The mathematics is written by AI

This is the first thing you should know, and it is not a disclaimer buried at the bottom. The statements and proofs here are drafted by large language models working from published mathematical sources, then checked by other models, then read by a human before anything is published. No step of that is a guarantee of correctness, and you should read this library the way you would read a careful but unfamiliar author: the argument is on the page, so check it.

Because “written by AI” covers very different things, every item carries two separate provenance labels — one for the statement and one for its proof. A theorem taken from a textbook and proved locally is not the same object as a claim a model invented, and the library refuses to blur them: an AI-generated statement may never be used as a load-bearing dependency by anything else.

How something gets published

Every item passes a mechanical gate that parses the proof format, resolves every declared dependency, checks the dependency graph stays acyclic, and renders the LaTeX to catch errors invisible in source. Then two independent AI judges from different model families read the item and its cited dependencies as adversarial refuters, trying to break the proof rather than approve it. Their verdicts are recorded per item — 1,306 of 3,431published items currently carry a passing judge verdict. Finally a human reads and audits it. Publication is that last human step, not the judges’.

The whole per-level process is animated, step by step, in how a level is built.

What this library does not claim

Some results are recorded but not proved here: the library states them with a citation because other results need them, but it does not prove them itself. 66 published items are marked that way, in fuchsia with a ‡, and so is everything downstream of them — because a proof resting on such a result inherits that gap. 233 items cite material developed later in the reading order; those are marked separately, in sky with a ↗, along with their consequences.

Both markers exist so you never have to guess which dependencies were actually established here. If you find an error — and in a corpus this size there will be errors — every item has a Report an issue control that sends it straight to us.

Licence and cost

Everything here is free to read, with no account and no paywall, and the content is licensed CC BY-SA 4.0 — see the licence page for what that means in practice. If you would like to help cover the compute the judging and audit passes consume, the support page explains how; nothing on this site is or will be gated behind it.