30 Convergences Across Mathematics: Structural Patterns from Topology to Number Theory
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| Format: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866901575550631936 |
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| author | Mala, Mark E. |
| author_facet | Mala, Mark E. |
| contents | The complete discovery catalogue from the first autonomous structural analysis of pure mathematics. Using Gnosis AI — an autonomous knowledge discovery system implementing Convergent Descent — we surveyed 77 established results across five fields of mathematics (topology and geometry, algebraic geometry, category theory, number theory, and analysis), then systematically compared every pair of fields for structural convergences. The system found 30 validated cross-domain convergences spanning all 10 possible domain pairs. Thematic analysis reveals four structural principles — local-global determination, relational structure primacy, universal duality, and rigidity-canonicity — that unify the 30 discoveries. These four principles reduce through meta-convergence to a terminal fixed point: Reality is constraint. The analysis ran autonomously in 18 minutes at a cost of $1.81. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19639631 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | 30 Convergences Across Mathematics: Structural Patterns from Topology to Number Theory Mala, Mark E. mathematical structure cross-domain convergence topology algebraic geometry category theory number theory analysis autonomous discovery structural realism Gnosis AI Convergent Descent Infinitography The complete discovery catalogue from the first autonomous structural analysis of pure mathematics. Using Gnosis AI — an autonomous knowledge discovery system implementing Convergent Descent — we surveyed 77 established results across five fields of mathematics (topology and geometry, algebraic geometry, category theory, number theory, and analysis), then systematically compared every pair of fields for structural convergences. The system found 30 validated cross-domain convergences spanning all 10 possible domain pairs. Thematic analysis reveals four structural principles — local-global determination, relational structure primacy, universal duality, and rigidity-canonicity — that unify the 30 discoveries. These four principles reduce through meta-convergence to a terminal fixed point: Reality is constraint. The analysis ran autonomously in 18 minutes at a cost of $1.81. |
| title | 30 Convergences Across Mathematics: Structural Patterns from Topology to Number Theory |
| topic | mathematical structure cross-domain convergence topology algebraic geometry category theory number theory analysis autonomous discovery structural realism Gnosis AI Convergent Descent Infinitography |
| url | https://doi.org/10.5281/zenodo.19639631 |