Truth Without Comprehension: A BlueSky Agenda for Steering the Fourth Mathematical Crisis
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914050417360896 |
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| author | Yu, Runlong Jia, Xiaowei |
| author_facet | Yu, Runlong Jia, Xiaowei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Truth Without Comprehension: A BlueSky Agenda for Steering the Fourth Mathematical Crisis Yu, Runlong Jia, Xiaowei Emerging Technologies 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. |
| title | Truth Without Comprehension: A BlueSky Agenda for Steering the Fourth Mathematical Crisis |
| topic | Emerging Technologies |
| url | https://arxiv.org/abs/2509.17290 |