A NewScientist article summarizes a new paper by philosopher and AI expert Aaron Sloman that appears in Artificial Intelligence journal. Sloman has been working on understanding how children develop mathematical understanding and believes it should be possible to create a robot designed to work the same way. He notes, "humans brains don't work by magic, so whatever it is they do should be doable by machine." To figure out how to do it by machine, Sloman has been identifying exactly which capabilities a child's brain uses to grasp mathematical ideas. He sites numerous examples where simple empirical childhood experiences spark understanding of specific mathematical principles; playing with cups teaches the brain transitivity and topology. For more on Sloman's work, check out his webpage on toddler theorems.