Abstract
Mathematics is an underexplored domain of human cognition. While many studies have focused on subsets of math concepts such as numbers, fractions, or geometric shapes, few have ventured beyond these elementary domains. Here, we attempted to map out the full space of math concepts and to answer two specific questions: can distributed semantic models, such a GloVe, provide a satisfactory fit to human semantic judgments in mathematics? And how does this fit vary with education? We first analyzed all of the French and English Wikipedia pages with math contents, and used a semi-automatic procedure to extract the 1,000 most frequent math terms in both languages. In a second step, we collected extensive behavioral judgments of familiarity and semantic similarity between them. About half of the variance in human similarity judgments was explained by vector embeddings that attempt to capture latent semantic structures based on cooccurence statistics. Participants’ self-reported level of education modulated familiarity and similarity, allowing us to create a partial hierarchy among high-level math concepts. Our results converge onto the proposal of a map of math space, organized as a database of math terms with information about their frequency, familiarity, grade of acquisition, and entanglement with other concepts.
Author summary Most studies in mathematical cognition focus on subdomains such as numbers, fractions, or geometric shapes. A broader picture of the full extent of mathematical cognition is lacking. Here, as a first step, we use behavioral and computational methods to create a comprehensive vocabulary of advanced math. We prove that statistical cooccurence vectors from large corpora (Wikipedia) provide an approximation of the meaning and organization of these concepts, as measured by human similarity ratings in participants of varying levels of education. Results are similar in French and in English, suggesting that our findings do not depend on the language. In future work, we plan to leverage this vocabulary to explore the brain mechanism of math cognition at various levels of expertise.
Competing Interest Statement
The authors have declared no competing interest.
