If learning maths requires a teacher, where did the first teachers come from?
Why (and how) did biological evolution produce mathematicians?
Presentation at Symposium on Mathematical Cognition AISB2010
Part of the Meta-Morphogenesis Project. See also this discussion of toddler theorems:
Evolution of human mathematics from earlier abilities to perceived, use and reason about affordances, spatial possibilities and constraints.
The necessity of mathematical truth does not imply infallibility of mathematical reasoning. (Lakatos).
Toddlers discover theorems without knowing it. Later they may learn to reflect on and talk about what they have learnt. Compare Annette Karmiloff-Smith on "Representational re-description".
Why is it still so hard to give robots and AI systems the ability to reason spatially as mathematicians do (except for simple special cases, e.g. where space is discretised.)