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PreprintarXiv licencearXiv

Math for AI safety: an invitation for mathematicians

  • Lionel Levine
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Abstract

Artificial intelligence threatens to outrun human understanding and control. New mathematics is needed to design AI that is legible, steerable, and cooperative with humanity. I organize this invitation by mathematical field, so you can turn straight to your own: logic and game theory for cooperation; probability for agency and world-models; algebra and representation theory for learned features; analysis and geometry for generalization and training dynamics. Each section ends with an open problem that is accessible to a working mathematician with no prior experience in AI safety.

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Cite

BibTeXRIS
BibTeX
@misc{levine2026math,
  title = {{Math for AI safety: an invitation for mathematicians}},
  author = {Lionel Levine},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15289},
  eprint = {2609.15289},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15289},
}
RIS
TY  - UNPB
TI  - Math for AI safety: an invitation for mathematicians
AU  - Lionel Levine
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15289
UR  - https://arxiv.org/abs/2609.15289
AB  - Artificial intelligence threatens to outrun human understanding and control. New mathematics is needed to design AI that is legible, steerable, and cooperative with humanity. I organize this invitation by mathematical field, so you can turn straight to your own: logic and game theory for cooperation; probability for agency and world-models; algebra and representation theory for learned features; analysis and geometry for generalization and training dynamics. Each section ends with an open problem that is accessible to a working mathematician with no prior experience in AI safety.
ER  -