### Why I Am Not a Mathematician

Thus V. I. Arnol'd, author of Mathematical
Methods of Classical Mechanics, Ergodic Problems of
Classical Mechanics, Topological
Methods in Hydrodynamics, etc., co-discoverer of the KAM
theorem, etc., in his little book on Catastrophe Theory
(pp. 109--110 of the 3rd English edition):

Unfortunately, the unsophisticated texts of Poincaré are difficult for
mathematicians raised on set theory. Poincaré would have said: "The
line divides the plane into two half-planes," where modern mathematicians write
simply: "The set of equivalence classes of the complement
R^{2}\R^{1} of the line R^{1} in the plane
R^{2} defined by the following equivalence relation: two points A, B
\in R^{2}\R^{1} are considered to be equivalent if the line
segment AB connecting them does not intersect the line R^{1}, consists
of two elements" (I am quoting by memory from a schoolbook).

The reason I am not a mathematician is not that I can't understand the
second version, it's that I wouldn't *automatically* translate it into
the first.

**Update, 28 August 2004**: Jay Han points me to a
wonderful lecture by Arnol'd "On Teaching
Mathematics".

Mathematics

Posted at August 27, 2004 06:59 | permanent link