134 A History ofMathematics
inspiration of Plato or Archimedes, saw the transformation in terms of the introduction of ‘math-
ematical language’, in a variety of senses, into the study of the natural world. True, mathematics
had been present for a long time, in astronomy and optics and in Archimedes’s statics, for example.
However, Galileo’s statement was explicitly expansionist (as well as being related to dynamics,
his particular interest): you will have founded a proper science only if you have introduced the
mathematics which is its hidden language.2. Literature
In almost every preceding chapter, we have complained of the difficulty of locating sources,
either primary or secondary or both. With the scientific revolution, we have the opposite prob-
lem. The major questions about the revolution (did it happen? what was its nature? what were
its causes?) have been constantly debated, and have spawned a vast literature, which even
specialists will find overwhelming. And the literature is easily accessible; the classic works of
Duhem, Butterfield, Koyré, Dijksterhuis, and Kuhn are much easier to find in libraries than
most of the other works I have recommended so far.^1 The same goes for many of the primary
sources, most obviously Galileo’s works. Help is at hand in the form of H. Floris Cohen’s recent
book (1994). Cohen is not particularly interested in the development of mathematics, and his
account is if anything too painstaking, but he does describe the major currents in the history,
the authors and texts who are worth further reading. Still, the literature continues to grow,
and new theses and new material are continually coming to the forefront in the discussion.
The reader should be prepared to keep a number of disparate, even conflicting ideas in mind
(e.g. about the origin of Galileo’s dynamics) at the same time—which is no bad thing for the
historian.
About the mathematics specifically, the literature is much slimmer; even for key figures like
Galileo and Kepler, the mathematical work generally takes second place to the physics. The most
interesting and detailed discussion is hard to recommend: dealing specifically with the ‘algebraic
aspect’ of the revolution, it is Jacob Klein’s very dense and detailed book (1968), a translation of
a German text of the 1930s. Despite its title, the key arguments of this book centre on what was
revolutionary in the algebra of the period 1550–1650, and I shall be referring to them, but it is not
easy to find, not very user-friendly, and (naturally) underestimates the Islamic contribution. All of
these criticisms are frankly acknowledged by Klein in his author’s note, but the problems remain.
More recently, Hadden (1994), which draws on Klein for some key ideas, is less detailed and more
polemical, but a relatively easy read.^2 The extracts in Fauvel and Gray are helpful, and there is
a special section which throws light on early modern England—which we shall not deal with, but
which is worth looking at.
Besides the problem of literature, we have a problem of timescale. Where do we start? The
seventeenth century propagandists, of whom Galileo and Descartes were the most persuasive,
tended to present their work as marking a clean break from a past of ignorance and sterile muddle-
headed scholastic disputes. The Greeks—some of them—were precursors, to be sure, but no one
else needed to be considered. This view was generally accepted as the history of science developed
- As the key example of a ‘revolution’, the period is central in the writing of Kuhn and of his opponents, naturally.
- See the review inIsis 86 (1995), pp. 642–3 for a criticism of this book’s attempts to have it both ways on Marxism in particular.