Assuming that my memory serves me nicely there are a couple of articles
-- concerning some of the questions you raise below -- in the Proceedings
of the second Portuguese-Brazilian meeting on the history of mathematics
and Second national seminar on the history of mathematics (1997). I vaguely
recall that Sergio Nobre (editor of the _Anais_) addresses a brief but
juicy note on the history of historiography of mathematics, and Ivor
Grattan-Guinness does a similar job in his _Five gains, five gaps_. I have
(temporarily!) lent my copy to a friend... so Sergio, Ubi, or other
colleague, could you please comment whether my recollections are correct?
Many thanks for your help.
Greetings from sunny Montevideo,
Julio Gonzalez Cabillon
PS: An interesting piece on metahistory is also that of Jesper Luetzen
and Walter Purkert - "Conflicting tendencies in the historiography of
mathematics: M. Cantor and H. G. Zeuthen" (pp 1-42) in "The history of
modern mathematics. Volume III: Images, ideas, and communities", eds.
Eberhard Knobloch et al., Boston, MA: Academic Press, 1994.
Christoph J. Scriba reviewed it for ZfM
[ online text at http://www.emis.de/cgi-bin/MATH-item?813.01011 ]
as follows:
"Cantor and Zeuthen may, in a certain sense, be considered
incarnations of two different approaches and ways of thinking
in the history of mathematics. On the one hand, we have an
encyclopedist who tries to unite a multitude of sources and
opinions into a comprehensive picture of the development of
mathematics and to integrate these into the evolution of human
civilization, underestimating thereby, to a certain degree,
an analysis of the inner logical components in the development
of mathematical ideas. On the other hand, we have a penetrating
mathematician who contributes to the history of mathematics by
examining the mathematical content of the works of the most
important scholars of the past and by showing the logical
connection between them. In the case of Cantor and Zeuthen
these different approaches led to a rather polemical scientific
dispute which also influenced their personal relations. Zeuthen
was the only famous historian of mathematics who did not
contribute to the Festschrift dedicated to Cantor on his 70th
birthday."
These words open the third section of this detailed study of two
outstanding historians of mathematics who both died in 1920. The
first section is devoted to Moritz Cantor (born 1829), whose
fundamental "Vorlesungen ueber Geschichte der Mathematik" (1880-
1908) have never been supplanted by a similar work. In the second
section the life and historical work of the excellent geometer
Hieronymus Georg Zeuthen is described in similar detail, while
section three on the Cantor-Zeuthen dispute serves to illuminate
the conflicting positions. Equipped with ample references, this
paper ought to be studied by everybody interested in the
methodology of the history of mathematics.
There are tons of references on historical studies of math history, but our
lovely beach is 200 meters away! ;-) So I leave to other friends to provide
further references, or better, insightful comments - I'm sure they will!
-JGC
In a message dated 8 Feb 1999, Alfred Ross wrote:
>
> I'm interested in the 'historical study' (and philosophical aspects)
> of historiography of mathematics. This may include:
>
> + The study of the evolution of research methods
> + New subfields (within math history) that have been opened
> up during this century (ethnomathematics, for instance)
> + The weight of (or different sensitivity to) 'interpretation'
> + Whiggism
> + The different approach to minority groups
>
> Paul J Cohen once put it
>
> This is our fate, to live with doubts, to pursue a subject
> whose absoluteness we are not certain of, in short to realize
> that the only "true" science is itself of the same mortal,
> perhaps empirical, nature as all other human undertakings.
>
> How historians have handled this "mortal nature" in their general
> histories or papers? Is there any research essay to this respect?
>
> What other issues ought to be considered part of a history/philosophy
> for 'math history'?
>
> Comments or references are appreciated.