Personality traits can offer considerable insight into the biological basis of individual differences. However, existing approaches toward understanding personality across species rely on subjective criteria and limited sets of behavioral readouts, which result in noisy and often inconsistent outcomes. Here we introduce a mathematical framework for describing individual differences along dimensions with maximum consistency and discriminative power. We validate this framework in mice, using data from a system for high-throughput longitudinal monitoring of group-housed male mice that yields a variety of readouts from across the behavioral repertoire of individual animals. We demonstrate a set of stable traits that capture variability in behavior and gene expression in the brain, allowing for better-informed mechanistic investigations into the biology of individual differences.