∴THE PROOF ATLAS
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A CARTOGRAPHY OF IDEAS

Mathematics is not a tree.
It is a history of crossings.

Explore 150 domains and the landmark arguments that carried an idea from one territory into another.

imported idea → target domain

Drag to pan · scroll to zoom · select any node or route

SCOPE & METHOD

A map, not a border treaty.

There is no canonical list of mathematical domains. This atlas uses the MSC2020 taxonomy—63 top-level, 529 intermediate, and 6,022 detailed classes—as its backbone, then consolidates it into named fields a mathematician might plausibly claim as a research identity.

An arrow means: methods characteristic of the source field were instrumental in a famous result whose central question belongs to the target field. It does not claim sole influence, priority, or a permanent one-way relationship.

150named domains
15constellations
27proof stories
—directed routes

READING THE ATLAS

Nodes are fields.
Arrows are intellectual travel.

The faint ellipses group neighboring domains. A bright route begins in a field that supplied a characteristic method and points toward the field containing the result’s central problem.

Select a route for its story and source. Select a domain to see every route touching it. Search dims everything else.

Edges are curated historical interpretations, not bibliometric measurements. The graph emphasizes celebrated cross-domain proofs; it is intentionally not a graph of every relationship in mathematics.