Finally I located my copy the proceedings of the second Portuguese-
Brazilian meeting on the history of mathematics and Second national
seminar on the history of mathematics (1997). And in fact there is
a couple of articles on historiography and metahistory, as I suggested.
This book must be very rare, since I receive 0-input on my request of
help -- or should I think otherwise?!
I will comment upon Grattan-Guinness's article "General Histories of
Mathematics? Of Use? To Whom?" written in honour of Wilbur R. Knorr.
1. How general is general?
Ivor Grattan-Guinness begins the article remarking that the three
questions posed in the title were stimulated by his recent work on
"editing and writing general studies for a wide (academic) public".
He is referring to "Companion Encyclopaedia of the History and
Philosophy of the Mathematical Sciences", published in a 2 volume
set (1806 pages, Amazon's price USD 325.00 !) by Routledge in January
1994. He goes on to say that after an editorial introduction, the
"Companion Encyclopaedia" is divided into 13 parts:
1 Non-Western traditions up to Western superventions
2 Medieval and Renaissance, up to Around 1600-1700
3 Calculus and analysis
4 Functions, series, and methods in analysis
5 Logics, set theories, foundations of mathematics
6 Algebras and number theory
7 Geometries and topology
8 Mechanics and mechanical engineering
9 Physics and mathematical physics, and electrical engineering
10 Probability and statistics, and the social sciences
11 Higher education and institutions
12 Mathematics and culture
13 Reference and information
This Encyclopaedia is so expensive (to us) that our libraries do
not seem to be quite happy to buy it. Could those of you familiar
with it, please, express your opinion of it? Pros and cons ... Thank
you very much for your sincere remarks!
Let me point out that, in this article, Grattan-Guinness hardly
answers his questions. A table of content, and a mention that the
work involved many colleagues to produce 176 articles, hardly cast
new light on what I was expecting. The questions sound as if he
were interested in introducing his "Companion Encyclopaedia" to
his colleagues at the seminar, as well as his subsequent single
volume (817 pages, ca. USD 32,5) "The Norton History of the
Mathematical Sciences: The Rainbow of Mathematics" -- First US
edition 1998, originally published in England under the title
"The Fontana History of the Mathematical Sciences: The Rainbow of
Mathematics", Fontana Press, May 1997. The chapter titles are:
1 Pre-viewing the rainbow
2 Invisible origins and ancient traditions
3 A quiet millennium: from the early Middle Ages
into the European Renaissance
4 The age of trigonometry: Europe, 1540-1660
5 The calculus and its consequences, 1660-1750
6 Analysis and mechanics at centre stage, 1750-1800
7 Institutions and the profession after the French Revolution
8 Mathematical analysis and geometries, 1800-1860
9 The expanding world of algebras, 1800-1860
10 Mechanics and mathematical physics, 1800-1860
11 International mathematics, but the rise of Germany
12 The rise of set theory: mathematical analysis, 1860-1900
13 Algebras and geometries: their relations and axioms, 1860-1900
14 An era of stability: mechanics, 1860-1900
15 An era of media: mathematical physics, 1860-1900
16 The new century, to the Great War and beyond
17 Re-viewing the rainbow
!! 1 volume ( 817 pages, ~ USD 32.50)
2 volumes (1806 pages, ~ USD 325.00) !!
Ivor G-G ends his paragraph 1 stating that "in a purportedly general
history, 'general' should be taken seriously, with applications granted
their proper place. Does current research match this range? What
novelties have come to light recently, and which topics remain under
the shadows, whether applied or not?"
What do you think? ...
2. Five gains, five gaps
This is precisely the paragraph I had in mind when I suggested the
reference to Alfred Ross in a previous posting to the list.
"The history of mathematics has a curious history of its own;
ups and down, with a strong period from around 1880 to the
Great War of 1914-1918."
This seems to me highly opinionated (and somewhat misleading).
I really do not think, for instance, that Baldassarre Boncompagni
(1821-1894) would be quite glad to agree with the said statement
after having published his monumental 20-thick-and-heavy-volume-set
of the _Bulletino di bibliografia e storia delle scienze mathematiche
e fisiche_ (Rome, 1868-1887). This is just an example, and I may as
well defend G-G opinion that Boncompagni's work is included in the
"up" movement. In Spanish we say: con que biblioteca quieres que
te defienda hoy? [something like "what thesis/bibliotheca should I use
to argue today?"]
Again G-G is highly subjective when he implies that nothing to write
home about occurred "until the early-mid 1970s when a revival began
rather rapidly, and is still in progress". A footnote here remarks that
"a group of historians working under the leadership of C.J. Scriba and
J.W. Dauben is producing a book on the history of mathematics up to the
1960's". [ Christoph, are you listening? If so, would you mind telling
us when this work is supposed to appear, and also other relevant details.
Thanks! ]
Do you (members of HM forum) agree with G-G? Usually is hard or better
painful to disagree with somebody like G-G, who has an immense prestige
amongst the math-history community. I agree. But the big question is
do you agree?...
Let me point out that "the early-mid 1970's" is not a random phrase. It
is obviously linked with the creation of the journal _Historia Mathematica_
in 1974. But what has happened to the prestigious _Archive for History
of Exact Sciences"? Very early in the 1960's my 'favourite periodical'
aimed to give "rapid and full publication to writings of exception depth,
scope, and permanence" in the historical research of the mathematical
sciences.
Curiously enough, G-G fails to mention this 'petit' detail, despite the
fact that he seems to defend the thesis (which I wholeheartedly agree)
that the place of physical applications in the history of mathematics
has been badly treated in general (exceptions are to confirm the rule).
I do not agree with other issues G-G mentions in this very paragraph, but
they are too local to comment upon it here. Let us save bandwidth.
Let me mention now the five gains (according to Grattan-Guinness):
1 Research on non-European mathematics
2 Mathematical education and institutions
3 Greater sensitivity to anachronisms in interpretation
4 The study of development since 1880
5 The study of probability and mathematical statistics
And here goes the five gaps:
1 Roman mathematics (curiously ignored)
2 Trigonometry (no general history since von Braunmu"hl)
3 Folkloric mathematics (eg clothes: *How* were the shapes determined?)
4 School education (content of books, curriculum planning, ...)
5 Place of physical applications in the history of mathematics
Any additions, corrections, criticisms, thumbs-up, are welcome!
Enough for now.
Regards to all,
Julio Gonzalez Cabillon