The working premise is narrower than a universal mathematics: difficult problems are often blocked not only by missing tools, but by disciplinary separation, incompatible vocabularies, inaccessible representations, and the cost of recognizing which existing formal machinery applies.
MOONSHOTS · Formal tools across disciplinary boundaries
Mathematical Interoperability
Make more of the mathematics and formal machinery that already exists across disciplines practically translatable, composable, and testable.
OBJECTIVE03 / 08
PROGRAMMoonshots
STATUSLong-horizon research goal
IMPORTANT LIMITThis is a direction, not a completed result.
This page describes the goal, work that already exists, and the main unresolved problems. It does not claim scientific validation, deployed capability, external adoption, market value, or inevitability.
Moonshots indexWHAT THIS GOAL MEANS TODAY
The current interpretation, footholds, and open problems.
AI is useful here as a search and translation layer across formal dialects, but the mathematics remains the constraint. The research burden is to state what a translation preserves, weakens, strengthens, introduces, forgets, or breaks.
Translation must expose loss
Interoperability burden
A useful crossing should say more than that two disciplines use similar words or diagrams.
- 01
Declare the native objects on both sides before translating.
- 02
Name preserved invariants and any structure that is weakened or forgotten.
- 03
Distinguish equivalence, compatibility, reduction, analogy, and convenience.
- 04
Test composition rather than isolated pairwise resemblance.
- 05
Compare against competent native methods and retain counterexamples.
PROGRAM CONTEXT