Human infants can discriminate between different small numbers of items, and can determine numerical equivalence across perceptual modalities. This may indicate the possession of true numerical concepts. Alternatively, purely perceptual discriminations may underlie these abilities. This debate addresses the nature of subitization, the ability to quantify small numbers of items without conscious counting. Subitization may involve the holistic recognition of canonical perceptual patterns that do not reveal ordinal relationships between the numbers, or may instead be an iterative or 'counting' process that specifies these numerical relationships. Here I show that 5-month-old infants can calculate the results of simple arithmetical operations on small numbers of items. This indicates that infants possess true numerical concepts, and suggests that humans are innately endowed with arithmetical abilities. It also suggests that subitization is a process that encodes ordinal information, not a pattern-recognition process yielding non-numerical percepts.