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arXiv · 2509.17290

Truth Without Comprehension: A BlueSky Agenda for Steering the Fourth Mathematical Crisis

Runlong Yu·Xiaowei Jia
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Abstract

Machine-generated proofs are poised to reach large-scale, human-unreadable artifacts. They foreshadow what we call the Fourth Mathematical Crisis. This crisis crystallizes around three fundamental tensions: trusting proofs that no human can inspect, understanding results that no one can fully read, and verifying systems that themselves resist verification. As a minimal yet principled response, we propose the Human Understandability (HU) meta-axiom, which requires that every proof admits at least one projection that is resource-bounded, divergence-measured, and acceptable to a verifier. Confronting these questions opens a timely research agenda and points toward new directions in scalable reasoning, interpretable inference, and epistemic trust for the era of machine-scale mathematics.

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Runlong Yu, Xiaowei Jia. 2025-09-22. Truth Without Comprehension: A BlueSky Agenda for Steering the Fourth Mathematical Crisis. https://arxiv.org/abs/2509.17290

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