[FOM] Are proofs in mathematics based on sufficient evidence?

Michael Barany michael.barany at tellurideassociation.org
Wed Jul 14 03:12:49 EDT 2010

> Can you point me towards a good source that argues for this thesis,
> which provides good textual examples/evidence of what you refer to as
> the text becoming detached from the original meaning?


The paper that introduced me to this kind of historiography was a
somewhat obscure one by Jens Hoyrup called  "The formation of a myth:
Greek mathematics---our mathematics" from a bilingual volume from 1996
titled L'Europe mathematique / Mathematical Europe.  Catarina's
recommendation of Netz's volume is a good one,... it doesn't really
talk about how Greek geometry (and deduction in general) has been
rendered by Europeans, but it reconstructs a version of what might
count as its "original meaning" which appears quite alien to anyone
with a conventional present-day view of Euclid.  Amir Alexander edited
a special section of the history of science journal Isis in 2006 on
the topic of narratives in mathematics, and Joan Richards'
contribution gives a particularly good view of changing notions of
rigor (including Euclidean rigor) between the 18th and 19th centuries
in France.  Both Alexander and (especially) Richards have written
extensively on these questions in recent years.  Douglas Jesseph has a
very entertaining account of Hobbes's doubling of the cube in the
journal Studies in the History and Philosophy of Science 30(3), 1999.
I have a paper under review right now which discusses Cauchy's
re-interpretation of Euclid in his Course in Analysis (1821).  Beyond
Euclid, there are many good examples in the history of science
literature of texts having widely varying meanings in different
periods; for instance, our understanding of Origin of Species differs
in many aspects today from that of scientists in the 1920s or in the
1870s, with many differences not attributable merely to "better
understanding of evolution" (e.g. our view today of the work's
relevance to human societies is a lot closer to those from the 1870s
than those from the 1920s).  You may have encountered Foucault's
phrase "the death of the author" which, regardless of what one makes
of Foucault, has been an enormously influential concept in the field
of history (basically, the author does not have ultimate control over
how a work is read; this can even be applied to highly logical or
formulaic works, such as can be found in mathematics).

Hopefully this selection of papers gives a good outline of the theory.
 I do not know of any comprehensive "history of rigor" that takes this
approach, although I would very much welcome one and may even aspire
to write such a thing if the opportunity presents itself in the
not-too-distant future.



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