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An atom is one small thing a learner can do: solve a pair of simultaneous equations, add fractions with different denominators. School maths is about two thousand of them.

We let an AI that can see read two maths textbooks, page by page. 757 pages, £55. Everything it found on a page was checked against everything it had found so far and came back with a verdict: new, reuse, or refine. A new idea, an idea it already had, or an idea it already had that this page said better. That is why the catalogue grows fast at the start and slowly at the end: by the later chapters, most of what a page teaches has already been seen.

The result is 1,934 atoms joined by 4,616 links saying what has to be learned before what. Click any atom in the cloud to see what it is, what it needs, and what needs it.

The links are the point. Every question a child answers marks the atoms it used as held or not held, and the links then say what that child is ready for next: whatever needs only atoms they already hold. That decision never mentions age. A nine-year-old who holds the prerequisites for simultaneous equations is ready for them; a fourteen-year-old missing one atom from primary school goes back and picks it up. Each child walks this map at their own pace.

To find out more about how this system works and what it enables, read the paper.