Report on the ICHM Special Session in Honour of the Retirement of Henk Bos:
The Henk Bos Valedictory Symposium
Utrecht, June 30, 2005
by Jan Hogendijk
Henk Bos giving his valedictory lecture
The symposium was focused around the retirement of
Henk Bos as full professor of History of Mathematics
on July 1, 2005.
The symposium was opened by Jan Hogendijk, who called attention to the ICHM sponsorship. The first speaker was Annette Imhausen (Cambridge, UK).
In her lecture, entitled "Administration, Education, Representation: The Various Uses of Mathematics in Ancient Egypt," Dr. Imhausen presented
a survey of the different periods of the history of ancient Egypt, the types of surviving mathematical evidence, and the conclusions which can be
drawn on the mathematical activities in each period. The fragmentary nature of
the evidence was marvellously illustrated.
After the lunch break,
Volker Remmert (Mainz, Germany) gave a presentation entitled
"Antiquity, Nobility and Utility:
Picturing the Mathematical Sciences in the Early Modern Period."
Using illustrations from
mainly frontispieces of sixteenth and seventeenthcentury
mathematical works,
the speaker took the audience on a recreational tour through the "garden of mathematics." Remmert discussed the iconography of ancient and early
modern mathematicians and astronomers
(all males), and of mathematics and her branches
(arithmetic, geometry, stereometry etc.), all depicted as females,
as well as the messages implied in this iconography.
The high point of the symposium was the traditional "afscheidscollege"
(retirement lecture) by Henk Bos, titled "Loose Ends."
In his lecture, Henk Bos examined the Leibnizean concept of
"infinitangular polygon" as an example of a "fluid concept."
A fluid concept is a concept which cannot be precisely defined and
which may be selfcontradictory. Important key concepts in history of
mathematics are fluid concepts. These concepts cannot be precisely
reconstructed from the surviving sources and cannot be exactly
analyzed in modern mathematical
terms. The fact that some of the
important basic concepts in mathematics are fluid concepts
is an argument against the supposed unshakable truth of mathematics.
The valedictory lecture was immediately followed by
"Unconcluding remarks" by Jeremy Gray (Milton Keynes, UK).
Gray began with an analysis of Henk Bos' historical metholodology,
which then turned into a ceremony in which the Kenneth O. May Medal was
presented to Henk Bos.
Kirsti Andersen and Henk Bos listening to
the beginning of Jeremy Gray's "unconcluding remarks"
Henk Bos realizing that he was getting the Kenneth O. May Medal
Jeremy Gray presenting the fifth Kenneth O. May Medal to Henk Bos
Text of the Citation read by Jeremy Gray (for Karen Hunger Parshall, Chair, ICHM)
In 1989, the International Commission for the History of Mathematics awarded
for the first time the Kenneth O. May Prize in the History of Mathematics.
This award honors the memory of Kenneth O. May, mathematician and historian
of mathematics, who was instrumental in creating a unified international
community of historians of mathematics through his tireless efforts in
founding in 1971 the International Commission for the History of Mathematics
and in 1974 the ICHM's journal, Historia Mathematica. The Kenneth O. May
Prize has been awarded every four years since 1989 to the historian or
historians of mathematics whose work best exemplifies the high scholarly
standards and intellectual contributions to the field that May worked so
hard to achieve. To date, the following distinguished historians of
mathematics have been recognized for their work through receipt of the
Kenneth O. May Prize, which includes a medal cast in bronze and designed by
the Canadian sculptor, Salius Jaskus:
 in 1989, Dirk J. Struik (United States) and Adolf P. Yushkevich
(Soviet Union);
 in 1993, Christoph J. Scriba (Germany) and Hans Wussing (Germany);
 in 1997, René Taton (France); and
 in 2001, Ubiratàn D'Ambrosio (Brazil) and Lam Lay Yong
(Singapore).
On behalf of the International Commission for the History of Mathematics, it
is my great pleasure to present the 2005 Kenneth O. May Prize and Medal to
Henk Bos (The Netherlands).
Henk Bos earned his Ph.D. from Utrecht University in 1973 for a dissertation
entitled "Differentials, Higher Order Differentials and the Derivative in
the Leibnizian Calculus." This major study, which appeared in the
Archive
for History of Exact Sciences under that same title in 1974, was the first
to draw attention to, and explain, what Leibniz's differentials actually are
and how they were used; in so doing, it illuminated several otherwise
puzzling features of the Leibnizian calculus.
By 1981, Bos's research interests had shifted to the roles of geometry and
algebra in the work of Descartes. In that year, he published another major
work "On the Representation of Curves in Descartes' Géométrie" and then
three years later yet another fundamental study on "Arguments on Motivation
in the Rise and Decline of a Mathematical Theory: The 'Construction of
Equations,' 1637ca. 1750," both again in the
Archive for History of Exact
Sciences. It is not, however, the careful reading of all of Descartes's
relevant writings that makes these works stand out (although selective
readings are the norm). Nor is it the attention to the decline of a
mathematical theory that is particularly noteworthy in Bos's research,
although that too is unusual in a field often given over to the celebration
of accomplishment. Rather, it is the steady force of his critical intellect
that makes his research exceptional. He took a subject—the invention of
Cartesian geometry, which most historians of mathematics thought they
knew—and showed that they did not know it. He accomplished this in the best
historical tradition, namely, by reading the historical texts carefully on
their own terms. He examined Descartes's conceptions both of a curve and of
how properly to answer geometrical questions. He then showed how these
conceptions governed the formation of Descartes's remarkable work and how
they shaped considerations of such questions for a century. Finally, he
documented how these ideas waned as the original rationale behind them
ceased to convince.
This body of work earned Henk Bos a professorship of the history of
mathematics in 1985 at Utrecht University where he has, indeed, spent his
entire career. The very next year, in 1986, his work was again recognized
when he was honored as an invited speaker at the International Congress of
Mathematicians held in Berkeley, California. Many of the historical issues
that he had addressed up to this point were collected in a book of essays,
entitled Lectures in the History of Mathematics, which was published in 1993
and reprinted in 1997 in the HMATH series of the American and London
Mathematical Societies. A volume well regarded by mathematicians, who find
in him a trustworthy writer of mathematics, it has effectively extended
Bos's audience beyond the community of historians of mathematics to the
international mathematical community as a whole. These essays document a
further feature of his work: the enormous pleasure he takes in what he
writes about, and which he invariably conveys.
In 2001, Bos's longawaited book, Redefining Geometrical Exactness:
Descartes' Transformation of the Early Modern Concept of Construction, was
published by SpringerVerlag. A work of exceptional distinction, it greatly
extends and refines his earlier analysis of Descartes, in addition to
considering seriously the responses that other scholars have made to his
historical research. It looks at Descartes's contemporaries and immediate
predecessors: Clavius, Viète, Kepler, and Fermat; it is deeply versed in
the
sources, as good history should be; yet, its most profound characteristic is
its thoughtfulness. Bos gives to this seventeenthcentury material the kind
of careful attention it was given by the experts when it was new. It is an
exploration of what counted as good mathematics in a particular period and
is crafted, as its title suggests, around the concept of exactness. When is
a mathematical description exact? What sorts of constructions are to be
allowed? This is, dare one say, "exactly" the right question to ask. The
result is a book that not only recaptures a major aspect of the mathematics
of its time but also strongly suggests how much more good work can be done
elsewhere in the history of mathematics provided the historian has the
ability to ask such a good question and to pursue its answers so
sensitively.
Henk Bos has, through his deep and insightful research, fundamentally shaped
presentday understanding of the mathematics of the seventeenth century. It
is for this accomplishment that the International Commission for the History
of Mathematics is proud to present to him the 2005 Kenneth O. May Prize and
Medal.
