Seeking a Language in Mathematics 1523-1571

Seeking a Language in Mathematics 1523-1571

Bruce Marsden<br>Scope Cuthbert Tunstall, later Bishop of London and then Durham, published the first book on mathematics conceived and printed in England in 1523; it was a commercial arithmetic written in Latin. By the time of Thomas Digges's publication of his book on geometry in 1571, the use of English in mathematical publications and the practical arts' had become established, but not entirely to the exclusion of Latin. There is<br>a parallel, which may be aetiological, between the growth of the use of vernacular languages and the striking surge of mathematics in science in western Europe culminating during the seventeenth century in the works of Descartes, Galilei, Huygens and, particularly, Newton.

The period under consideration is the beginning of what has become known as the Scientific Revolution,[1] which is usually agreed to span about 1550-1700 and during which mathematics became the distinguishing discipline. Just as significant, however, is the bearing of mathematics on the evolution of technology with regard to the much later Industrial Revolution, from about 1750. Interaction between science and technology is another tale to tell, and there is an important overlap in the making of scientific instruments. In the first decades of the Scientific Revolution the most notable instruments were to do with navigation, which connects to cosmology and astronomy in one intellectual direction, and to the surveying of land and buildings in another. These bonds will become evident in the works of Robert Record (c.1510-58), John Dee (1527-1608), and Leonard c.1510-57) and Thomas (c.1543-95) Digges, the main authors considered in this essay. The languages (verbal and symbolic) for basic mathematics (arithmetic, geometry and algebra) were formed in principle, and the means whereby the languages were to be developed were broadly indicated.

In addition to the growth in the use of English for mathematical works, other related topics to be considered include: the value of such publications for artisans (Shakespeare's rude mechanicals'), and in education more widely; contributions to the English language from mathematics; developments within the study of mathematics of the use of mathematical symbols and notation; and the growth of knowledge and understanding in mathematics in theory and practice (formerly, and improperly, pure and applied mathematics).

Verbal and symbolic language The word 'language' is intended to mean one of two forms of communication. The first is the spoken and written language used in expressing the mathematical terms and operations; the second, the symbolic form of those terms and operations. This second treats<br>notation, formulae, calculations and suchlike and is — in so far as these are held in common — understood internationally, whereas the first is understood only by those who are familiar with the spoken or written language of address. As will be seen, the verbal symbolic languages often worked in harness, with the symbolic form growing extending its influence gradually throughout the period. The most important single for in this growth is the development of the use of mathematical equations, which to be transformed by the introduction of the sign for 'equals' — this by Recorde in 1557 but it was not until the next century that the effects of his innovation were to be found in the literature.

Mathematics in English It is a truism, but an important one none the less, to say that English was preserved and nurtured in the speech of the lower classes during the Middle Ages. By a process of linguistic osmosis in England English was becoming the main language of communication, ousting Anglo-Norman French in court and government circles, and competing with Latin in intellectual and theological affairs.

Following the introduction of movable-type printing in the latter half of the fifteen century, the movement gained considerably in momentum. Leonard Digges in 1556 wrote of the 'arte of numbring [which] hath been ...hyd and as it were locked up in strange tongues'[2] The strange tongues are primarily Latin, followed by French, Italian and German. But another tongue is the symbolic language of mathematics, a language frequently associated with the magic and sorcery.[3] In producing the early, and original, printed works on mathematical topics the verbal and symbolic forms were developed the same time in English once the groundwork had been established. This was done initially by direct and indirect translations, and also by transforming largely unwritten information used mainly in trade, commerce, and management of estates.

Before 1551 there was little innovation in the language of mathematics, as authors were mainly concerned with bringing into English concepts familiar though not written in English, and in translation from Latin and continental vernaculars at an elementary level on subjects which had a...