Nothing from Something: Can a Language Model Discover 0?

Computer Science > Artificial Intelligence [Submitted on 15 Jun 2026] Nothing from Something: Can a Language Model Discover 0? Phoebe Zeng, Thomas L. Griffiths, Brenden M. Lake AI systems based on artificial neural networks are being developed with aspirations of pushing the boundary of human mathematical knowledge. A key question for these systems is how much they can reach beyond their training data. Mathematical discovery requires a strong form of out of distribution generalization; the ability to hypothesize genuinely new - and potentially logically more powerful - mathematical structures. It has been hypothesized that language abilities support such generalizations in human cognition. In this work, we use simple arithmetic as a case study for examining how modern AI models could expand their mathematical horizons, evaluating whether these models can independently discover the concept of "zero". We show that We show that (1) language models of a GPT-2 size are unable to perform this generalization at test time regardless of language pretraining, but (2) models can improve substantially after training on tens or hundreds of examples of zero. Additionally, we find that language pretraining reduces the number of required examples by approximately 50\%, showing that language abilities can scaffold mathematical discovery in neural models. Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL) Cite as: arXiv:2606.17289 [cs.AI]   (or arXiv:2606.17289v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.17289 Focus to learn more Related DOI: https://doi.org/10.32470/vp0ddtg Focus to learn more Submission history From: Phoebe Zeng [view email] [v1] Mon, 15 Jun 2026 20:54:04 UTC (9,693 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs cs.CL References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)