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The proof no human has read

Global in scope·An enduring case

The 1976 proof of the four colour theorem relied on computer checking of hundreds of case configurations that no mathematician could verify by hand, and parts of the community initially refused it the status of proof. The theorem now stands, and the objection quietly became a definition question: proof for whom?

The concepts this raises

Each of these gives a class a different way into the same case.

JustificationGrounds of Knowledge
The reasoning that connects evidence to a conclusion. Two knowers can hold the same evidence and be justified in different beliefs if their inferential standards differ. Justification is what separates knowing something from happening to be right about it.
CertaintyStatus of Knowledge
The degree to which doubt about a claim has been closed off. Certainty is a state of the knower, not of the claim, which is why a claim can be true without anyone being certain of it and why confidence and reliability can come apart badly.

Where it sits in the knowledge framework

Methods and tools
The practices, conventions, instruments and forms of reasoning through which knowledge here is actually made, together with the assumptions those methods build in and what they are structurally unable to detect.

Areas of knowledge

Themes

The same ideas, somewhere else

Cases that raise a concept this one raises, but in a different area of knowledge or a different part of the world. That contrast is the point: it is what shows a student the concept travels.