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Ramanujan's unproven theorems

From India·An enduring case

Srinivasa Ramanujan filled notebooks with thousands of results, many stated without proof and attributed by him to intuition or the goddess Namagiri. Mathematicians spent the following century proving most of them correct. The results were true in 1914; the discipline could only call them knowledge later.

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.
InterpretationThe Knower's Lens
The work of making something mean something. Data, texts, images and events do not announce their own significance; the categories a knower brings determine what is even available to be noticed, which is why disagreements about interpretation are rarely settled by looking harder.

Where it sits in the knowledge framework

Perspectives
Whose viewpoints have shaped this knowledge, which viewpoints have been absent, and how the discipline handles internal disagreement. This element includes the historical dimension: how the standpoint of a field has moved over time.
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

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.