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Topic: Matheology § 249
Replies: 2   Last Post: Apr 15, 2013 3:11 PM

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Posts: 13,460
Registered: 1/29/05
Matheology § 249
Posted: Apr 15, 2013 7:36 AM
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Matheology § 249

When I was a first-year student at the Faculty of Mechanics and
Mathematics of the Moscow State University, the lectures on calculus
were read by the set-theoretic 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
The de-geometrisation 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
cake-and-apple example from Poincaré {{who used to name a disease a
disease too}}.
[V.I. Arnold: "On teaching mathematics" (1997), Translated by A.V.

Regards, WM

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