Mathematical competence can endow robots of the necessary capability for abstract and symbolic processing, which is required for improving their cognitive performance and their social interaction with human beings. But so far, only few attempts have been made to apply mathematical cognition in robots. The objective of the NUMBERS project is to construct a novel artificial cognitive model of mathematical cognition by imitating human like learning approaches for developing number understanding. This will provide a novel tool for developmental psychology and neuroscience research on the development of mathematical abilities in children. The objective will be achieved through a highly interdisciplinary research program that will take advantage of the collaboration of leading academics in the fields involved, prof. Cangelosi (Cognitive Developmental Robotics), Plymouth University, and prof. McClelland (Computational Psychology), Stanford University, USA, and the technical support of an industrial partner (NVIDIA Corporation, USA and UK). The NUMBERS' research activities will exploit the cutting-edge facilities offered by Sheffield Robotics, a joint initiative between the University of Sheffield and Sheffield Hallam University, which will host the project. Indeed, the model will be integrated with one of the most advanced child-like robotic platform (the "iCub") and, therefore, validated through realistic experiments, resembling scientific experiments of mathematical cognition in children. The validation of the novel model of the numerical cognition in interactive robotic experiments will constitute a proof of concept of the enhanced capabilities offered by a modular approach to bio-inspired artificial intelligence architectures. Furthermore, an optimised implementation for mobile devices will be realised in order to downsize space and power requirements for the computation, increasing application opportunities. This foundational research will provide the methodological basis and cognitively plausible engineering principles for the next generation of socially interactive robots, mimicking advanced capabilities of the human intelligence for real understanding and interaction with the external world. Results will help the design of more efficient cognitive robotic systems capable of learning abstract symbolic number processing in a more flexible and ecological manner. The human-like learning and interaction are characteristics that might allow people to more easily identify the desired social overture that the robot is making, or facilitate the transfer of skills learned in human-human interactions to human-robot encounters. This envisioned humanization will positively affect the acceptance of robots in social environments, as they will be perceived as less dangerous, increasing the socio-economic applications of future robots that can take on tasks once thought too delicate or uneconomical to automate. This is particularly relevant in the fields of social care, companionship, therapy, domestic assistance, entertainment, and education.