Generative syntax and a consistently ordered count routine are both understood to have central roles in learning a number system. However, there has been little experimental exploration of how the diversity of each of these features alters the inductive landscape of number learning, as most empirical work has been constrained to correlational studies. We present a causal manipulation both of syntactic structures and counting procedures, using an artificial language paradigm. Our findings suggest that (1) learners have a greater facility with conjunctive over multiplicative rules of composition, (2) counting procedures help learners to recall words independently of syntax, and (3) predictable syntax helps learners to use numerical concepts, independently of - and possibly despite - counting routines.

Symbolic representations of number are instrumental to mathematical reasoning and many aspects of social organization. What explains their emergence in human cultures? To understand how functional and cognitive constraints impact people’s communication about number, we used a drawing-based reference game to investigate how human dyads coordinated to form novel number systems. We found a systematic bias towards symbols exploiting 1-to-1 correspondence to objects in visual arrays, and that this strategy was contingent on the communicative relevance of number. Moreover, the meaning of these symbols was transparent to third party observers not present during their production. Finally, model-based analyses of these symbols' visual properties suggest that the ability to decode exact quantity from them may rely on perceptual processing mechanisms beyond those sufficient for object recognition. These findings contribute to our understanding of how both communicative need and capacity for visual abstraction constrain the emergence of iconic representations of exact number.