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Invited talkLittle green men from Mars and other thought experiments in philosophy of mathematics. Professor Alexandre Borovik, School of Mathematics, University of Manchester
We all know the notorious question: If little green men from Mars
existed, would their mathematics be the same as ours? In a less joky
form, the question can be restated in the ethnographic context, with
reference, among other examples, to:
We can also shift back in time for 500 years and be able to add to all this diversity---which was likely to be already in existence at that time---two parallel and apparently independent "advanced" systems of mathematics which in both cases included emerging calculus: European and Kerala. After that, the question: "Do different cultures produce different mathematics?" becomes highly non-trivial.
In my talk, I will add to the list of examples another forgotten tribe of humanity: children. Using responses from my fellow mathematicians who recall difficulties that they encountered in their early learning of mathematics, I'll try to answer the question: "is the mathematics that children learn the same as the mathematics that is taught to them"?