This is the latest progress report on a long term quest to defend Kant's philosophy of mathematics. In humans, and other species with competences that evolved to support interactions with a complex, varied and changing 3-D world, some competences go beyond discovered correlations linking sensory and motor signals. Dealing with novel situations or problems requires abilities to work out what can, cannot, or must happen in the environment, under certain conditions. I conjecture that in humans these products of evolution form the basis of mathematical competences. Mathematics grows out of the ability to use, reflect on, characterise, and systematise both the discoveries that arise from such competences and the competences themselves. So a "baby" human-like robot, with similar initial competences and meta-competences, could also develop mathematical knowledge and understanding, acquiring what Kant called synthetic, non-empirical knowledge. I attempt to characterise the design task and some ways of making progress, in part by analysing transitions in child or animal intelligence from empirical learning to being able to "work things out". This may turn out to include a very general phenomenon involved in so-called "U-shaped" learning, including the language learning that evolved later. Current techniques in AI/Robotics are nowhere near this. A long term collaborative project investigating the evolution and development of such competences may contribute to robot design, to developmental psychology, to mathematics education and to philosophy of mathematics. There is still much to do.
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