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What makes a theorem interesting? Operationalizing interestingness for open-ended exploration — arXiv:2611.02905

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02905
License (as archived): CC0-1.0
Archived: 2026-11-03T10:44:10.039Z
SHA-256 of the archived text: e40aeb5468f113d4c56c459a19f46f35fdadc33357e4b5ca4afb0756ca2ccb99
Stable URL of this page: https://metraipolis.com/documento/dc_da12a41fa7af

How to cite

What makes a theorem interesting? Operationalizing interestingness for open-ended exploration — arXiv:2611.02905 — arXiv (en), https://arxiv.org/abs/2611.02905 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_da12a41fa7af (Metraipolis archive dc_da12a41fa7af, sha256 e40aeb5468f113d4c56c459a19f46f35fdadc33357e4b5ca4afb0756ca2ccb99)

BibTeX

@misc{dcda12a41fa7af,
  title = {What makes a theorem interesting? Operationalizing interestingness for open-ended exploration — arXiv:2611.02905},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02905},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_da12a41fa7af; sha256 e40aeb5468f113d4c56c459a19f46f35fdadc33357e4b5ca4afb0756ca2ccb99},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02905. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

An agent that explores, whether it generates conjectures or research ideas, must decide which of them are worth keeping. This judgment of interestingness is usually delegated to a hand-picked proxy or to a language model, neither of which is known to correspond to what humans actually value. I study it for mathematical theorems, by observing which results mathematicians single out in formal libraries and in papers. I model each way of singling out results as an evaluator that weights features of a result's statement, its proof and dependencies, and split its weights into a shared and a subjective part. In formalized mathematics, ex-ante features predict these selections as well as a large language-model judge, and the two complement each other. Interestingness is also largely shared. One set of weights, carried mostly by structural features such as the length of the statement and of the proof and the subfields the proof draws on, accounts for most of the signal and transfers in part across formal libraries. What remains subjective depends on practices and individual authors more than on subfields. The judge's advantage lies in its knowledge of the canon, and neither the judge nor the features rely on memory of the papers. The approach, which infers what a community finds interesting from what it singles out, can be applied to other sciences.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2611.02905 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T10:39:50.323Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).