A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Models

The evolution of mathematics has been guided in part by interestingness. From researchers choosing which problems to tackle next, to students deciding which ones to engage with, people's choices are often guided by judgments about how interesting or challenging problems are likely to be. As AI systems, such as LLMs, increasingly participate in mathematics with people -- whether for advanced research or education -- it becomes important to understand how well their judgments align with human ones. Our work examines this alignment through two empirical studies of human and LLM assessment of mathematical interestingness and difficulty, spanning a range of mathematical experience. We study two groups: participants from a crowdsourcing platform and International Math Olympiad competitors. We show that while many LLMs appear to broadly agree with human notions of interestingness, they mostly do not capture the distribution observed in human judgments. Moreover, most LLMs only somewhat align with why humans find certain math problems interesting, showing weak correlation with human-selected interestingness rationales. Together, our findings highlight both the promises and limitations of current LLMs in capturing human interestingness judgments for mathematical AI thought partnerships.

Minding the Politeness Gap in Cross-cultural Communication

Misunderstandings in cross-cultural communication often arise from subtle differences in interpretation, but it is unclear whether these differences arise from the literal meanings assigned to words or from more general pragmatic factors such as norms around politeness and brevity. In this paper, we report three experiments examining how speakers of British and American English interpret intensifiers like "quite" and "very." To better understand these cross-cultural differences, we developed a computational cognitive model where listeners recursively reason about speakers who balance informativity, politeness, and utterance cost. Our model comparisons suggested that cross-cultural differences in intensifier interpretation stem from a combination of (1) different literal meanings, (2) different weights on utterance cost. These findings challenge accounts based purely on semantic variation or politeness norms, demonstrating that cross-cultural differences in interpretation emerge from an intricate interplay between the two.