Das Kalenderblatt 100607

06/06/2010 - 07:00 von WM | Report spam
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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#1 honghanru
07/06/2010 - 08:47 | Warnen spam
On 6月6日, 上午7时00分, WM wrote:
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. GORYUNOVhttp://pauli.uni-muenster.de/~munsteg/arnold.html

Gruß, WM



Hallo,

es war einmal dunkle Zeit, manche Mathematiker ,die nichts von Physik
verstanden und Physiker, die nichts von Mathematik verstanden, die
waren nicht in der Lage von den WERKEN von Euler und Gauß zu
verstehen. aber sie wollten trotzdem sich hoch einbilden. Sie
dichteten Unsinn wie Mengelehre oder Relativtheorie.

sochen Unsinn könnten trotzdem behaupten, weil die Generation dumm und
faul waren. sie interessierten sich auch nicht für die Wahrheit.

aber Lügen ist wie Papier, wie schön auch darauf gemahlt ist, Wahrheit
ist wie Feuer, wie schwach die auch scheint.


Grüße,

Fei

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