Mathematical thinking and its development: A machine learning approach

Data Science Seminar

Sashank Varma
Georgia Tech

Abstract

Mathematical thinking is a fundamental aspect of human cognition. Cognitive scientists have investigated the mechanisms that underlie our ability to thinking geometrically and numerically, to take two prominent examples, and developmental scientists have documented the trajectories of these abilities over the lifespan. In this talk, I explore what computer vision (CV) models can tell us about whether mathematical concepts are ‘built in’ or whether they are learnable through experience in the world. I present recent studies showing that CV models trained on the unrelated task of image classification learn ‘for free’ latent representations of geometry, topology, and number similar to those of adults. Building on this demonstrated cognitive alignment, I consider the question of developmental alignment: Do CV models increase in mathematical sensitivity over training, and does this increase match the developmental trajectories observed in children? For geometric and topological concepts, there is developmental alignment for some classes (Euclidean geometry, geometrical figures, metric properties) but not others (chiral figures, symmetrical figures). For number, there is developmental alignment in the emergence of a human-like ‘mental number line’ representation with experience. These findings reveal the promise – and the limitations – of using CV models to understand mathematical development, and point the way to future work evaluating newer models and assembling larger benchmarks.