Applied ↔ pure math bridge
- From applied to pure: strip the units and the noise; identify the underlying space, operator, or PDE.
- From pure to applied: pick a regime (small/large parameter, generic vs degenerate), then connect the abstract theorem to a measurable prediction.
- Sanity-check the bridge with a toy version of the real problem before scaling up.
- Be explicit about which idealizations matter and which are harmless.