This may be of interest to some!
JOHN BIBBY
-----Original Message-----
From: [log in to unmask]
[mailto:[log in to unmask]] On Behalf Of Julio
Gonzalez Cabillon
Sent: 13 November 1998 23:49
To: HISTORIA MATEMATICA
Subject: [HM] Marx and mathematics (was: Sophie Germain & Carl Boyer)
At 06:37 PM 13/11/1998 -0500, Guy F. Brandenburg wrote:
>
> What did Karl Marx contribute in mathematics? That's a new one for me!
>
Dear Guy F. Brandenburg,
Much has been written about Marx's affair with mathematics (in the same
guise, perhaps, that chess researchers have handled the issue of Napoleon's
interest in chess). The most recent paper on the subject is "Marx, Mao and
Mathematics: The Politics of Infinitesimals" addressed by Joseph Warren
Dauben at the ICM 1998, and published in _Documenta Mathematica_ (Journal
der Deutschen Mathematiker-Vereinigung), Extra Volume ICM III, pp. 799-809,
1998. The abstract follows:
The "Mathematical Manuscripts" of Karl Marx were first published
(in part) in Russian in 1933, along with an analysis by S. A.
Yanovskaya. Friedrich Engels was the first to call attention to
the existence of these manuscripts in the preface to his Anti-Du"hring
[1885]. A more definitive edition of the "Manuscripts" was eventually
published, under the direction of Yanovskaya, in 1968, and subsequently
numerous translations have also appeared. Marx was interested in
mathematics primarily because of its relation to his ideas on
political economy, but he also saw the idea of variable magnitude as
directly related to dialectical processes in nature. He regarded
questions about the foundations of the differential calculus as a
"touchstone of the application of the method of materialist dialectics
to mathematics." Nearly a century later, Chinese mathematicians
explicitly linked Marxist ideology and the foundations of mathematics
through a new program interpreting calculus in terms of nonstandard
analysis. During the Cultural Revolution (1966-1976), mathematics
was suspect for being too abstract, aloof from the concerns of the
common man and the struggle to meet the basic needs of daily life in
a still largely agrarian society. But during the Cultural Revolution,
when Chinese mathematicians discovered the mathematical manuscripts
of Karl Marx, these seemed to offer fresh grounds for justifying
abstract mathematics, especially concern for foundations and critical
evaluation of the calculus. At least one study group in the Department
of Mathematics at Chekiang Teachers College issued its own account of
"The Brilliant Victory of Dialectics - Notes on Studying Marx's
'Mathematical Manuscripts'." Inspired by nonstandard analysis,
introduced by Abraham Robinson only a few years previously, some
Chinese mathematicians adapted the model Marx had laid down a century
earlier in analyzing the calculus, and especially the nature of
infinitesimals in mathematics, from a Marxist perspective. But they
did so with new technical tools available thanks to Robinson but
unknown to Marx when he began to study the calculus in the 1860s. As
a result, considerable interest in nonstandard analysis has developed
subsequently in China, and almost immediately after the Cultural
Revolution was officially over in 1976, the first all-China conference
on nonstandard analysis was held in Xinxiang, Henan Province, in 1978."
Fortunately enough you may read the whole article online at
http://www.emis.de/journals/DMJDMV/xvol-icm/19/19.html
I would be happy to provide further references if you are definitely
interested in the subject.
Enjoy!
Julio GC
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