From Alexandria, Through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in Honor of J.L. Berggren

583 Pages·2014·576.719 MB·English

by  J. Lennart Berggren (auth.), Nathan Sidoli, Glen Van Brummelen (eds.)

Part I
Surveys
From Alexandria, Through Baghdad

Nathan Sidoli
Glen Van Brummelen
Editors
From Alexandria, Through Baghdad
Surveys and Studies in the Ancient Greek
and Medieval Islamic Mathematical Sciences
in Honor of J.L. Berggren
Editors
Nathan Sidoli Glen Van Brummelen
School for International Li beral Studies Quest University
Waseda University Squamish
Tokyo, Japan British Columbia, Canada
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For Len

An Appreciation
After a full lifetime in academia, one learns to appreciate colleagues who have a great sense of humor,
who do not take themselves too seriously, and who are enthusiastic about life both within and away from
the academy. One especially learns to appreciate these characteristics since they have become so rare.
With the rise of over-specialization, the ever-increasing market drive in colleges and universities, and
the regrettable incursion of competitive pressures for career advancement, academicians are becoming
more inward focused and less committed to their colleagues and their institutions. Fortunately, there
are still "throw-backs" to an earlier tradition and Len Berggren personifies all that is positive in that
tradition.
My first acquaintance with Len was in the spring of 1983, when I had organized the first meeting
of what became the Columbia History of Science Group. As an organizational neophyte, I had invited
people to attend the meeting, but had neglected to require pre-registration or any other form off inancial
commitment. Thus, after I had reserved the meeting space, the accommodations, and the catering
requirements, I found myself on the financial hook for the entire bill. I was expecting twenty-five
attendees, but soon the cancellations began to trickle in at the last moment, cancellations that pointed
toward personal financial ruin. When the numbers had shrunk to twenty, I knew my assistant professor's
salary was in real trouble. Then Professor Berggren from Simon Fraser drove up in his Volvo, not alone,
but with his lovely wife Tasoula and their two young boys. With twenty-three attendees, I broke even!
Although I had not previously met Professor Berggren, I was immediately drawn to Len and his
family, but not just because they saved my bank account. First of all, his last name and choice of
automobile both indicated that Len and I shared the same nationality (Sweden}. Then, the manner
in which the f.unily interacted gave a dear indication that here was an academic who cared more for
his family than his career. Indeed, the four Berggrens seemed genuinely excited to be together and
also seemed to enjoy each other's company. Finally, when Len presented his paper on some arcane
subject ofa ncient mathematics-indeed, probably ancient Islamic mathematics!-his entire family was
in the audience. I was soon to learn that Tasoula, with her roots in the eastern Mediterranean basin,
was an active collaborator with Len in his work and that the sons, too, knew of their parents' academic
interests.
But I have not commented on Len's wonderful sense of humor and, above all, his personal humility.
Since our auspicious meeting in 1983, I have had the pleasure of spending a long weekend at Friday
Harbor with Len almost every yt:ar. One of the traditions we have had at our meeting is that the annual
Milosian speaker never materializes (indeed, we always invite someone who cannot, for many reasons,
attend the meeting}. But Len was not in on the joke and, one yt:ar, volunteered to give the evening
talk. With slides and a prepared talk, no one could bear to tell Len that the talk was designed not to be
given. But in a way, the joke was on all of us, since Len gave a very engaging talk, all the time poking
fun at the academic enterprise and providing us all with a heightened sense ofe nlightenment and levity.
Len and Tasoula are also gracious hosts and superb companions. When I moved to Vancouver, they
invited me to spend a weekend in their mountain condominium at Whisder. It was a real pleasure to
be with Len in such a relaxed setting. Walking, fishing, visiting, and laughing were all high on the
agenda. And since I am not an historian of mathematics, nor an ancient scholar, nor an expert on
Islamic science, our conversations were hardly on the professional level. But that is what makes Len
such a wonderful person. He is a remarkable scholar, but above all, he is a wonderful human being and
one person for whom I am enormously grateful to have known.
Vancouver, October 2010 Keith R. Benson
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Preface
The practice of the history of mathematics is in flux. This statement may seem ironic or even para
doxical, for a discipline that relies seemingly on logic and precision. However, trends in the scholarly
practice of history are gradually causing substantial changes in the questions raised by practitioners
of the discipline, and the methods used to try to arrive at answers. Fifty years ago the discipline was
populated mostly by mathematicians, emphasizing logical reconstructions and explanations; today, the
concerns of the historian are being heard. Surprisingly, nowhere are these changes more true than in
the study of ancient Greek mathematics, which has seen precious little genuinely new source material
come to light in the past decades. Debates concerning, for instance, how to consider the Greek notion
ofg eometric algebra led to an increasing realization that even mathematical structures can be shaped by
cultural perspective; therefore, modern reconstructions of ancient concepts contain the hidden danger
of saying as much about the historian as about the history.
With respect to medieval Islamic mathematics, the manuscript situation is entirely different: hun
dreds or even thousands of texts remain in libraries, unedited and not yet easily available to the scholar.
Nevertheless similar trends have been felt. Categorizing subdisciplines according to our modern math
ematical perspective is rightly viewed with suspicion. The border between mathematics and science was
entirely different, and subjects like astrology need to be placed in a context appropriate for its time,
not ours. The assumption of a single Islamic mathematical culture has been criticized, and nuanced
evaluations of different mathematical communities are starting to arise. Even the traditional focus on
the best theoretical mathematics of the time period has been questioned, raising the need to clarify
the purpose of studying the history of mathematics in the first place. Is our primary task to provide a
plausible logical path that led to the present mathematics, or should we rather be concerned with how
mathematics clarifies the human condition within and between different cultures?
The literature accompanying these shifts in perspective has been vast, and negotiating the terrain can
be difficult even for a scholar in these areas, let alone a new graduate student or an interested outsider.
We are thus truly fortunate that a small tradition of surveys of the current state of the art, both in
Greek and in Islamic mathematics, was initiated in the 1980s by J. Lennart Berggren. His 1984 survey
of Greek mathematics (the first article in this volume), followed by a 1998 survey by Ken Saito (the
second article), vividly tell the story of changing foci and perspectives. On the Islamic side, Len's 1985
and 1997 surveys (the fourth and fifth articles) tell the story of a vast literature coming to light, and
the interaction of different points of view in coming to grips with it.
These four articles, so helpful to us as developing scholars, have not received updates since then
(other than a couple of surveys in particular subdisciplines). As a fitting tribute to a man so important
to us, and as a vital service to new scholars, graduate students, and interested readers, we have brought
these four papers together in this volume, and written two new survey papers (one Greek, and one
Islamic) to take the narrative to the present day. Through this we hope to provide a handbook or
guide to developments in the field over the past forty years. In addition, we hope that the combined
bibliographies oft hese articles, some 900 entries altogether, can form a kind ofp aper database to provide
a guide to the recent practice of the discipline. They also bear witness to the shifts in perspective that
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