Lenses and Waves

LENSES & WAVES 263
mathematical physics without bothering too much about their mutual
connections or their theoretical and philosophical background. As a result of
Huygens’ pragmatism or eclecticism, his oeuvre may sometimes seem like a
mishmash of isolated problems, brilliantly yet pragmatically solved. If we
expect a brilliant savant to be searching for new or better foundations,
Huygens may indeed pose a problem. Elaborating and applying theories does
not yield new foundations. This makes it difficult to situate him among the
Galileos and Newtons.
Yet, Huygens’ pre-1670s oeuvre has historical significance in several
other respects. It reveals another aspect of modern science, the application
of mathematics to concrete things. Huygens’ mathematics was the kind of
the rational mechanics that was to develop in the course of the eighteenth
century. 12 I have the impression that this kind of science tends to be
overlooked by historians of science. When it comes to the scientific
revolution, they primarily look at the development of new conceptual and
methodological foundations. 13 As regards seventeenth-century optics this is
evident: whereas the discovery of the sine law and of dispersion as well as
the mathematization of the corpuscular nature of light have amply been
studied, the development of geometrical optics as cultivated by Huygens in
Dioptrica has received hardly any attention.
Historians seem to feel a bit awkward about the fact that someone of the
stature of Huygens was a mere problem solver. Some have tried to distill
some kind of underlying philosophical scheme from his activities. 14 I do not
expect that seeing him as some kind of neo-Cartesian will shed more light on
the character of his oeuvre. 15 I am more taken by the fact that a seventeenthcentury
savant of his stature was so unprogrammatic and displayed such a
lack of interest in epistemological, methodological and philosophical issues.
Those historians tend to overlook that this problem solving for the pleasure
of problem solving has historical significance in its own right. It made
Huygens into one of the first – perhaps the very first – of a new kind of
scientist, an investigator of nature desiring to do things better than others,
12 Mulder, “Pure, mixed and applied mathematics”, 37-39.
13 This has also been suggested by Gabbey, at the 1979 symposium, in trying to understand why Huygens’
mechanics has received relatively little attention from historians: “…, I would suggest that historians have
clustered around Galileo, Descartes, or Newton because one of their central aims was to describe the
fundamental nature and workings of the physical world, and since this is the primordial purpose of
physical science, the concomitant difficulties and inconsistencies, the associated philosophical and
mathematical problems, the false starts, the anomalies, the blind allies, all the unfinished business, are
irresistible to the historian. By contrast, Huygens has been visited relatively infrequently by historians
because he solves problems, and does so magnificently, by an appeal to principles and hypotheses his
intuition and empirical sense tell him are right, rather than erect an explanatory system of the world that
has its roots in an original analysis of the nature of things.” Gabbey, “Huygens and mechanics” 175-176.
Fortunately, since 1979 the situation around Huygens’ mechanics has changed to the better with, first of
all, Yoder’s Unrolling time and, more recently, with Mormino’s ‘Penetralia motus’ .
14 Elzinga does so on the basis of Traité de la Lumière. Elzinga, On a research program.
15 Hall, “Summary”, 309-310.