Nothing from Something: Can a Language Model Discover 0?

This arxiv paper uses the concept of zero as a test case for whether language models can engage in genuine mathematical discovery—extending beyond their training distribution to recognize and work with a structurally novel concept. The findings are measured rather than triumphant: GPT-2-scale models cannot perform this generalization without additional training examples, but language pretraining does meaningfully reduce the number of examples required, suggesting that linguistic scaffolding has some role in supporting mathematical reasoning. It is careful, modest work that resists overclaiming, and that makes it worth reading in a field where overclaiming is routine.