Artificial Intelligence and the Autonomization of Mathematics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910264695193600 |
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| author | Ripoll, Jaime |
| author_facet | Ripoll, Jaime |
| contents | This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already present in the autonomization of Mathematics itself.
Modern Mathematics progressively developed formal environments that became increasingly autonomous, internally stable, and structurally navigable, reducing their dependence on concrete experience. In this context, the affinity between AI and contemporary mathematical practice appears less accidental than it may initially seem.
The essay also discusses possible limits of formal navigability, particularly regarding the emergence of genuinely new conceptual regimes and forms of mathematical intelligibility. Husserl's reflections on mathematization and the distancing of science from the Lebenswelt provide a broader philosophical framework for understanding this process.
We finally suggest that the contemporary debate on AI may concern less a threat to Mathematics itself than a challenge to the historical image of the mathematician as the privileged interpreter of mathematical structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27966 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Artificial Intelligence and the Autonomization of Mathematics Ripoll, Jaime Differential Geometry 00A30, 68T01, 00A35 This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already present in the autonomization of Mathematics itself. Modern Mathematics progressively developed formal environments that became increasingly autonomous, internally stable, and structurally navigable, reducing their dependence on concrete experience. In this context, the affinity between AI and contemporary mathematical practice appears less accidental than it may initially seem. The essay also discusses possible limits of formal navigability, particularly regarding the emergence of genuinely new conceptual regimes and forms of mathematical intelligibility. Husserl's reflections on mathematization and the distancing of science from the Lebenswelt provide a broader philosophical framework for understanding this process. We finally suggest that the contemporary debate on AI may concern less a threat to Mathematics itself than a challenge to the historical image of the mathematician as the privileged interpreter of mathematical structures. |
| title | Artificial Intelligence and the Autonomization of Mathematics |
| topic | Differential Geometry 00A30, 68T01, 00A35 |
| url | https://arxiv.org/abs/2605.27966 |