This is indeed a daunting question and has no universal answer; any answer necessarily depends on the context – where is it being asked, and when, who is asking it and to whom. Even here, in the Edward Worth Library, whose extensive mathematical collection consists of about one hundred mathematics books, there are also gaps in the collection (for example, there is no mathematics from China or from Mayan culture). Of course, we should not expect any of these aspects of mathematics to arise in a collection that spans 200 years from the 1530s to the 1730s, embracing a cultural canvass of contemporary England, France and the Netherlands (and just a little further afield), and stretching back in time to other lands such as ancient Greece and renaissance Italy. Edward Worth’s collection reflects his abiding interest in all forms of European mathematics and provides us with a fascinating insight into early modern mathematics.

The mathematics in the Edward Worth Library, if at all it ‘belongs’ to any place can probably best be described as ‘English’, for the period (from Henry VIII to George II); certainly it is one characterized by the expansion and consolidation of English political power in Ireland, and the establishment of a confident Protestant (Anglican) Anglo-Irish elite. The collectors, John (1648-1688) and Edward Worth (1676-1733), were conscious of the larger world of mathematical printing, not just England, but Ireland too, and Amsterdam, Bologna, Copenhagen, Geneva, Leiden, Leipzig, Lyon, Mainz, Marburg, Paris, Rome, Venice, … This was the world of Edward Worth, and his legacy is part of Irish heritage.

As is evident from the oldest mathematical book in the collection, Cuthbert Tunstall’s *De arte supputandi libri quatuor* (Paris, 1538), English mathematics was in a poor state in the second third of the sixteenth century; over the next two centuries it would be utterly transformed. Preparing this exhibition has been an exploration of that transformation. This exhibition is structured with nine chapters (in addition to this introductory one). The titles of five of the nine come from the headings of the five parts of Ward’s *The Young Mathematicians Guide*. *Being a plain and easie Introduction to the Mathematicks* (London, 1719): Arithmetic, Algebra, Geometry, Conic Sections and Infinities.

Claud François Milliet Dechales, *Cursus seu Mundus Mathematicus* (Lyon, 1690), index.

As can be seen from the index of Dechales’ *Cursus seu Mundus mathematicus* (Lyon, 1690), the first four of these were standard fare in any contemporary comprehensive mathematical text. These headings also appear in Ozanam’s *Dictionnaire mathematique, ou, Idée generale des mathematiques* (Paris, 1691). It seemed that ‘Infinities’ opened a door into the more advanced mathematics of the period, the emergence of the calculus, represented here by Wallis, Brouncker and L’Hôpital. The other four chapters were determined by themes common to the books on which the students contributing to this exhibition worked: Probability, Applications, Notation and Communities.

It was sometimes difficult to assign a particular book to an exhibition chapter. For example, Descartes’ *Geometria* (Latin edition of 1659) surely belongs to Geometry, or Algebra or, maybe, Conic Sections. It seemed important to emphasize his contribution to revolutionising notation, and likewise for Viète and Harriot who could just as well have fitted into Algebra. Cardano might have featured in Probability, but we put him in Algebra, and ‘confined’ Probability to Huygens and Montmort. Wilkins, for his extraordinary machines, and Pascal, for his work on liquids and gases, were placed in Applications, while Fontenelle, with his eulogies, fitted well into Communities.

Returning to Ward’s ‘quindrivium’, Conic Sections features Archimedes and Van Ceulen, for their quadrature of the circle, yet accommodating all conic sections using the work of Apollonius (Commandino edition of 1566) and Robert Steell’s *A treatise of conic sections* (Dublin, 1723). For Geometry, almost the entire stage was given over to Euclid, and in three editions (Commandino, Barrow and Gregory). On the page below, in Ozanam’s work we see number theory and geometry combined.

Jacques Ozanam, *Dictionnaire mathematique, ou, Idée generale des mathematiques* (Paris, 1691), p. 30.

The Arithmetic chapter features the Tunstall’s *De arte supputandi* (Paris, 1538) and Leybourn’s *The art of numbring by speaking-rods: vulgarly termed Nepeirs bones* (London, 1667), while, in addition to Cardano in the Algebra chapter, we have John Kersey’s *The elements of that* *mathematical art commonly called algebra*, *expounded in four books* (London, 1673).

We finish this introductory chapter without having answered its question explicitly. We hope that visitors to Mathematics at the Edward Worth Library will enjoy the experience of browsing the pages and working with some of the problems that are presented. Be sure to contact us if you have interesting comments.

**Text:** Maurice OReilly.