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Matheology § 249
Posted:
Apr 15, 2013 7:36 AM


Matheology § 249
When I was a firstyear student at the Faculty of Mechanics and Mathematics of the Moscow State University, the lectures on calculus were read by the settheoretic topologist L.A. Tumarkin, who conscientiously retold the old classical calculus course of French type in the Goursat version. [...] These facts capture the imagination so much that (even given without any proofs) they give a better and more correct idea of modern mathematics than whole volumes of the Bourbaki treatise. [...] The emotional significance of such discoveries for teaching is difficult to overestimate. It is they who teach us to search and find such wonderful phenomena of harmony of the Universe. The degeometrisation of mathematical education and the divorce from physics sever these ties. [...] teaching ideals to students who have never seen a hypocycloid is as ridiculous as teaching addition of fractions to children who have never cut (at least mentally) a cake or an apple into equal parts. No wonder that the children will prefer to add a numerator to a numerator and a denominator to a denominator. From my French friends I heard that the tendency towards super abstract generalizations is their traditional national trait. I do not entirely disagree that this might be a question of a hereditary disease, but I would like to underline the fact that I borrowed the cakeandapple example from Poincaré {{who used to name a disease a disease too}}. [V.I. Arnold: "On teaching mathematics" (1997), Translated by A.V. Goryunov] http://pauli.unimuenster.de/~munsteg/arnold.html
Regards, WM



