Invited talk
Little green men from Mars and other thought experiments in philosophy of mathematics. Professor Alexandre Borovik, School of Mathematics, University of ManchesterWe 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:
* Tenejapan Tzeltal people of Central America who have no words or
concepts for the left and the right -- they live in square houses,
with a door (made of two equal halves) positioned in the middle of the
south wall;
* Guugu Yimithirr people of Australia who live in the absolute (and
Cartesian!) coordinate system and, when asked "where is the kettle?",
answer "two steps north of the fireplace";
* some tribes of Equatorial Africa who have no awareness of geometric
perspective (the list can be continued).
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"?