Identify foundational axioms to resolve the Fourth Mathematical Crisis

Determine which new foundational axioms should be introduced to address the Fourth Mathematical Crisis characterized by large, opaque, AI-generated proofs that challenge human trust, understanding, and verification, and specify their form and role in reconciling machine-checked correctness with human interpretability.

Background

The paper argues that mathematics is entering a "Fourth Mathematical Crisis" driven by machine-scale proofs that are too vast for human verification (Q1), too deep for human comprehension (Q2), and reliant on complex, layered computational stacks that resist complete audit (Q3). This situation fractures long-held assumptions that mathematical proofs should be fully surveyable and that verification tools are transparently reliable.

To navigate this crisis, the authors propose a Human Understandability (HU) meta-axiom, an epistemic infrastructure for making large proofs acceptable to bounded verifiers through resource-bounded, divergence-measured projections. However, they acknowledge that addressing the crisis may require new foundational axioms beyond existing systems, and explicitly state that what those axioms should be is currently unknown.