Mathematics is a part of physics. Physics is an experimental science,

a part of natural science. Mathematics is the part of physics where

experiments are cheap.

The Jacobi identity (which forces the heights of a triangle to cross

at one point) is an experimental fact in the same way as that the

Earth is round (that is, homeomorphic to a ball). But it can be

discovered with less expense.

In the middle of the twentieth century it was attempted to divide

physics and mathematics. The consequences turned out to be

catastrophic. Whole generations of mathematicians grew up without

knowing half of their science and, of course, in total ignorance of

any other sciences. They first began teaching their ugly scholastic

pseudo-mathematics to their students, then to schoolchildren

(forgetting Hardy's warning that ugly mathematics has no permanent

place under the Sun).

Since scholastic mathematics that is cut off from physics is fit

neither for teaching nor for application in any other science, the

result was the universal hate towards mathematicians - both on the

part of the poor schoolchildren (some of whom in the meantime became

ministers) and of the users.

The ugly building, built by undereducated mathematicians who were

exhausted by their inferiority complex and who were unable to make

themselves familiar with physics [...] predominated in the teaching of

mathematics for decades. Having originated in France, this

pervertedness quickly spread to teaching of foundations of

mathematics, first to university students, then to school pupils of

all lines (first in France, then in other countries, including

Russia).

To the question "what is 2 + 3" a French primary school pupil replied:

"3 + 2, since addition is commutative". He did not know what the sum

was equal to and could not even understand what he was asked about!

Another French pupil (quite rational, in my opinion) defined

mathematics as follows: "there is a square, but that still has to be

proved".

Judging by my teaching experience in France, the university students'

idea of mathematics (even of those taught mathematics at the École

Normale Supérieure - I feel sorry most of all for these obviously

intelligent but deformed kids) is as poor as that of this pupil.

For example, these students have never seen a paraboloid and a

question on the form of the surface given by the equation xy = z^2

puts the mathematicians studying at ENS into a stupor. Drawing a curve

given by parametric equations (like x = t^3 - 3t, y = t^4 - 2t^2) on a

plane is a totally impossible problem for students (and, probably,

even for most French professors of mathematics).

V.I. Arnold: "On teaching mathematics" (1997)

mathematics in Palais de Découverte in Paris on 7 March 1997.

Translated by A.V. GORYUNOV

http://pauli.uni-muenster.de/~munsteg/arnold.html

Gruß, WM

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