Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving cross-linguistic numeral systems, which humans can learn to solve successfully. We investigate why this task is difficult for LLMs through a series of experiments that untangle the linguistic and mathematical aspects of numbers in language. Our experiments establish that models cannot consistently solve such problems unless the mathematical operations in the problems are explicitly marked using known symbols (+, ×, etc, as in “twenty + three”). In further ablation studies, we probe how individual parameters of numeral construction and combination affect performance. While humans use their linguistic understanding of numbers to make inferences about the implicit compositional structure of numerals, LLMs seem to lack this notion of implicit numeral structure. We conclude that the ability to flexibly infer compositional rules from implicit patterns in human-scale data remains an open challenge for current reasoning models.

Inferences from adjective-noun combinations like “Is artificial intelligence still intelligence?” provide a good test bed for LLMs’ understanding of meaning and compositional generalization capability, since there are many combinations which are novel to both humans and LLMs but nevertheless elicit convergent human judgments. We study a range of LLMs and find that the largest models we tested are able to draw human-like inferences when the inference is determined by context and can generalize to unseen adjective-noun combinations. We also propose three methods to evaluate LLMs on these inferences out of context, where there is a distribution of human-like answers rather than a single correct answer. We find that LLMs show a human-like distribution on at most 75% of our dataset, which is promising but still leaves room for improvement.