Mathematical Life in the Dutch Republic
The late sixteenth and early seventeenth century was a time of great upheaval in the Low
Countries. The establishment of the Dutch Republic introduced a rather idiosyncratic state on
the European scene, by its division of power between the provinces and the Stadtholder. The
new state turned out to be fertile soil for innovative trade warfare, substantial cultural and
infrastructural initiatives, and new approaches in polity. This was also a time of radical changes in
the pursuit of mathematics. In the mathematical sciences all kinds of transformations were taking
place, like the development of algebraic approaches to geometrical problems and new methods of
measurement in astronomy and surveying. In addition mathematical activity expanded to new
domains like fortification and navigation. In recent years these developments have been subject
of important new historical research. It has become increasingly clear that early history of the
Dutch Republic and transformations in mathematics are closely connected. The fourth centenary
of the death of Ludolph van Ceulen on 31 December 2010 offers a suitable occasion to organize
a workshop on mathematical life in the Dutch Republic.
The life and career of Ludolph van Ceulen (1540-1610) provides an inspiring entry into the
history of mathematics and Dutch society around 1600. Van Ceulen arrived in the Low Countries
around the time of the start of the Dutch revolt in 1567 and his death roughly coincides with the
start of the Twelve Years’ Truce in 1609, when the Republic had been established and began to
expand its political and economical power. When Van Ceulen passed away in Leiden on
December 31 1610, he could look back upon a successful career in mathematics. Of German
descent, he found his way to Holland in the 1560s where he became a fencing and mathematics
master in Delft. Apparently he made a name for himself since in 1584 he was asked for advice on
a treatise on quadrature presented to the Stadtholder, William of Orange. This started a lifelong
engagement with determining the proportions of the circle. After having moved his business to
Leiden in the 1590s Van Ceulen made his mark as a mathematical authority, serving in advisory
commissions and publishing his treatise on the quadrature of the circle, Vanden Circkel (1596). In
1600 his reputation was confirmed when he was appointed as the first professor of Duytsche
Mathematique at the engineering school established by William’s son, Stadtholder Count
Maurice. After his death, the professor of mathematics at Leiden University, Willebrord Snellius,
translated Van Ceulen’s works into Latin, thus bringing his legacy to an international scholarly
audience.
The career of Ludolph van Ceulen raises interesting questions regarding the pursuit of
mathematics in the early Dutch Republic. Van Ceulen was a typical ‘practitioner’, making a living
with mathematics instruction and serving as an advisor on all kinds of technical issues. He
encountered a diverse circle of mathematically interested men, from practitioners like Adriaan
Anthonisz. and Simon Stevin to humanist scholars such as Joseph Scaliger and Willebrord
Snellius. They engaged with various mathematical topics, ranging from the quadrature of the
circle and the geometry of conic sections to hydrostatics, navigation and surveying. For these
men mathematics had different meanings and they engaged with it in various ways. What
mathematics did these men developed men and how did such a diverse group interact?
In this period, huge advances were made in the development of notations and symbolic algebra,
and new algebraic techniques were applied to solve problems of a geometrical nature. Algebraic
solutions for equations of third (and fourth) degree were by now known, but higher degree
equations could (and can) generally only be solved by numerical approximation. Numbers,
rational and irrational, were increasingly used to express lengths and areas in geometry, but not
without dispute about acceptability, which in itself lead to a re-evaluation of the number concept.
As a result the classical barrier between numbers and geometrical magnitudes had to be
transcended. Van Ceulen played an active part in these developments. As a ‘rekenmeester’ –
mathematics teacher – without a classical education, he was perhaps less hindered by the
limitations imposed by the classics. Yet he was in contact with a number of prominent scholars,
such as Adriaan van Roomen for whom he solved certain problems about regular polygons;
problems that were known to interest Viète as well. The career of Van Ceulen offers an
opportunity to study the relationships, exchanges and collaborations between mathematicians of
such different status and stature.
This circle of mathematicians operated within a quickly transforming society. The Dutch
Republic had just come into being and was in the middle of the revolt against Spanish rule. New
social and intellectual structures were created, from a system of fortifications to the establishment
of universities. The Duytsche Mathematique is a classic example of the value of mathematics to
the new state. It aimed to train a new brand of military engineers and surveyors, providing
practice-oriented instruction in mathematics in the vernacular. Still, training in elementary aspects
of mathematics was not uncontested and it remains to be seen how the aspirations of Stevin and
Maurice related to the interests and ideas of others involved, such as Adriaan Anthonisz. Also,
how did the engineering school compare to other institutions intended to give shape to the new
state? What place did mathematics have in the new university in Leiden, and what form did this
take? Van Ceulen’s career shows that mathematicians were actively engaged with the magistrates
giving shape to the burgeoning state. Mathematicians served on committees together with all
kinds of experts and administrators and were employed in all kinds of offices. This raises the
question what role mathematicians played in the formation of the new state and how they
functioned in the cultural and intellectual life of the early Dutch Republic.
Although the centre of this mathematical activity was Holland, it was linked to places abroad in
various ways. The men involved were of different backgrounds often bringing with them
international contacts which they maintained by correspondence and travel. Mathematicians too
often sought an audience beyond the walls of their cities and provinces and looked for patronage
abroad. Traffic and exchange between Holland and the other provinces was intense. It sometimes
took the form of collaborative work, such as the Frisian-Holland Practijck des Lantmetens of Sems
and Dou. Mapping the exchanges of Dutch mathematicians will shed light on the way their
interregional networks informed ‘Dutch’ mathematics. The importance of the circulation of
knowledge and the role of men of practice in these exchanges, in the development of early
modern science is being increasingly recognized in recent history of science. As a result of its
intensive trade activities, its wealth and relative tolerant culture, the Dutch Republic was a central
node in the European and global networks of knowledge circulation.
This workshop on mathematical life in the Dutch Republic aims at bringing together historians
of mathematics and historians of social and cultural history, as well as historians and
mathematicians. It aims at developing a synthetic perspective on the cultural history of
mathematics in the Dutch Republic in the late sixteenth and early seventeenth centuries, the
onset of the Dutch Golden Age. This workshop will result in new ways of understanding the
interplay between mathematical content and historical context during a period that was
constitutive for both the Dutch Republic and early modern mathematics. By inquiring into
mathematician’s circulation networks, this workshop ties in with the NWO-funded project,
involving the Huygens Institute and the Descartes Center, for the collection and digitalization of
early modern Dutch scholarly correspondence. The mathematical community in the Netherlands
will organize several activities to commemorate Van Ceulen, to which this workshop will add.
The workshop aims at facilitating exchanges between several scientific communities through
collective discussions on the theme the workshop advances. History of science, and of
mathematics particularly, tends to be a blind spot in social and cultural history. Vice versa,
historians of science and mathematics are not always sufficiently informed of the expertise and
research opportunities found in the vast field of general history. In addition to the
historiographical challenges presented by late-sixteenth-century mathematical culture, the groundbreaking developments that took place also offer interesting mathematics. Reflections from the
perspective of contemporary mathematics on both the mathematics involved and the wider social
and cultural dynamics will enrich the understanding of mathematical life in the early Dutch
Republic. The workshop brings together these communities of historians, historians of
mathematics and mathematicians, represented by the three organizers.
Organizers
Dr.ir. F.J. (Fokko Jan) Dijksterhuis.
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Associate Professor in History of Science and Technology. Department STePS (Science,
Technology and Policy Studies), University of Twente.
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Training: Applied Mathematics, Mathematics Teaching.
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Expertise: history of early modern mathematical sciences. Thesis (1999): Lenses and Waves.
Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century (Kluwer,
2004). Currently: NOW-VIDI project ‘The Uses of Mathematics in the Dutch Republic’.
Dr. C.M.J.M. (Charles) van den Heuvel.
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Senior Researcher. KNAW Virtual Knowledge Studio for the Humanities and Social
Sciences.
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Training: Architectural historian.
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Expertise: Simon Stevin; history of architecture; history of surveying and fortification;
history of cartography. Thesis (1991): ‘Papiere Bolwercken’, De introductie van de Italiaanse
steden- en vestingbouw in de Nederlanden (1540-1609) en het gebruik van tekeningen. Recent: ‘De
Huysbou’ A reconstruction of an unfinished treatise on architecture, town planning and civil engineering
by Simon Stevin (Edita, 2006).
Dr. (Steven) Wepster.
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Assistant Professor. Institute of Mathematics, University of Utrecht.
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Training: Nautical College, Mathematics, Mathematics Teaching
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Expertise: Van Ceulen; history of early modern mathematics, astronomy and navigation.
Thesis (2007): Between Theory and Observations, Tobias Mayer’s explorations of Lunar Motion
(1751-1755)