Nothing from Something: Can a Language Model Discover 0?
A new study investigates whether language models can independently discover the mathematical concept of zero. It finds that GPT-2 scale models fail at test-time generalization but improve substantially with few-shot training, and language pretraining reduces the required examples by about 50%, suggesting language abilities scaffold mathematical discovery in neural models.
[2606.17289] Nothing from Something: Can a Language Model Discover 0?
[Submitted on 15 Jun 2026]
Title:Nothing from Something: Can a Language Model Discover 0?
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Abstract: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
arXiv-issued DOI via DataCite (pending registration)
Related DOI:
https://doi.org/10.32470/vp0ddtg
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From: Phoebe Zeng [view email] [v1] Mon, 15 Jun 2026 20:54:04 UTC (9,693 KB)
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