Pub Date : 2020-03-09DOI: 10.1080/26375451.2020.1735618
Fenner Stanley Tanswell
we see how they generated, and were informed by the use of mathematics. Important scientific issues indicate the problems with traditional views, touching on the messy political and religious contexts. The characters involved are Tycho Brahe with critical observations, Kepler, who worked out the planetary orbits, and Galileo who observed and calculated and convinced people of a sun-centred universe. This is a ‘good read’ with both popular stories and serious content. By the early seventeenth century the actors were learning to adapt old methods to novel situations and invent new mathematics. Thus William Oughtred set out a more down-to-earth approach to learning, Girard Desargues founded projective geometry, Pierre de Fermat developed number theory, and René Descartes formulated his rational philosophy, science and mathematics. This last section is well-structured and interesting, but quite difficult for the less experienced; the authors are expecting the reader to do some serious work here. The final chapter acts as an overview, a reflection on the content and ambitions of the first thirteen chapters. One can approach the context of historical accounts as parts of a dialogue: whowere they writing to?What were they writing for (or about)? Andwe can also ask of the present volume, ‘What (or who) is this book for?’ The private scholar? The individual or college setting up a new course? But we must remember; this is not just a ‘history’ book. This book is a resource. It describes an optional course that was written for an undergraduate mathematics programme. From the introduction, we have: ‘We hope that [the book] will provide a rich introduction not only to the history of mathematics, but to mathematics itself ’ (pp 2–3). Despite the challenges, it succeeds admirably, and is highly recommended.
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Pub Date : 2020-02-12DOI: 10.1080/26375451.2020.1726050
C. Nothaft
The purpose of this article is to investigate the genesis and growth of a historical canard that can be encountered in numerous popular as well as some scholarly publications devoted to the history of mathematics. According to one of the core elements of this story, the number or symbol for zero was the cause of much anxiety in medieval Europe, as its unusual properties caused it to be associated with the Devil or with black magic. This anxiety is supposed to have extended to the entire system of Hindu-Arabic numerals, such that the use of these numerals was banned by the Church or by other powerful institutions. I shall argue that this narrative is false or unsubstantiated at nearly every level of analysis. Some elements arose from an unwarranted interpretation of medieval sources, while others are based on the unbridled imagination of certain modern authors.
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2019.1678821
J. Gray
One way to appreciate this multi-authored and multi-faceted book might be to see how it changes the picture of what we probably thought we knew, a picture that goes something like this. The Ecole P...
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2019.1701859
O. Bruneau
The Scottish scientist Colin Maclaurin (1698–1746) is mainly known as a mathematician who focused on pure mathematics. But during his life he was interested in the application of mathematics in all branches of knowledge. This article considers the relationships between theory and practice in Maclaurin's works.
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2019.1673101
A. Craik
The works of the Scottish natural philosopher George Sinclair (c.1630–1696) received far more criticism than praise, as described by (Craik, A D D, ‘The hydrostatical work of George Sinclair (c. 1630–1696): their neglect and criticism’, Notes & Records of the Royal Society, 72/3 (2018), 239–273), which focused mainly on Sinclair’s insightful account of hydrostatics. Here, we mention those few who influenced his work, and those who later commented upon it. His flawed account of the motion of pendulums, and the criticisms of it by James Gregory, are particularly examined.
苏格兰自然哲学家乔治·辛克莱（约1630–1696）的作品受到的批评远多于赞扬，如（Craik，A D D，“乔治·辛克莱的流体静力学工作（约1630-1696）：他们的忽视和批评”，皇家学会笔记与记录，72/3（2018），239–273）所述，主要集中在辛克莱对流体静力学的深刻描述上。在这里，我们要提到那些影响他的作品的少数人，以及后来对他的作品发表评论的人。他对钟摆运动的错误描述，以及詹姆斯·格雷戈里对它的批评，都受到了特别的审视。
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2020.1702651
Isobel Falconer
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2019.1684040
Martin Macbeath
Grand Vizier who appears in Chapter 5 with his demonstration of the power of exponentiation. The narrative is mostly European and USA-centric – Grand Vizier notwithstanding – and so it is somewhat surprising how US-biased the view of theoretical computing is. Awhole chapter is devoted to the topic of complexity theory, a notion of which is described as ‘the key to the most important idea in computer science’ (159): which seems odd, given that in Europe there is very little focus on complexity in a thriving theoretical computing community. One final slight niggle: throughout the book Steiglitz teases the notion that analogue computing machines might be capable of doing things that digital ones cannot. When this topic is directly addressed in Chapter 11, however, he is quite emphatic that this seems very unlikely. It is an odd sticking point in an otherwise very coherent book. In summary: The Discrete Charm of the Machine packs a lot of ideas into a rather slim and very readable work, nicely explaining most of the technical points that are involved in digital computing at a hardware level. There is a lack of detail in some places and too much in others, but overall the interested reader will find a lot to like here (and in the broad variety of suggested further reading): as long as they do not mistake it for a history book!
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2019.1701860
Davide Crippa
In this paper, I shall reconstruct the stay in Italy of James Gregory (1638–1675), Regius professor of mathematics at St Andrews. According to a standard account, Gregory spent four years (1664–1668) in Padua, as Stephano degli Angeli's student. However, this claim is problematic. First, Gregory's stay in Padua is confirmed only for the years 1667–1668. Second, the existence of a partial scribal copy of Vera quadratura circuli, ellipseos et hyperbolae in sua propria specie inventa et demonstrata, Gregory's debut work in the domain of quadrature problems, as well as a number of letters preserved at the National Library of Florence, suggest that relations between Gregory and Italian mathematicians were more complex and varied than have been suspected. On the basis of new, albeit scarce, textual evidence, I shall advance a few conjectures regarding scholars and philosophers that Gregory could have met in Padua, Rome and perhaps Florence.
在本文中，我将重现圣安德鲁斯大学数学教授詹姆斯·格里高利(1638-1675)在意大利的生活。根据一个标准的说法，格列高利在帕多瓦度过了四年(1664-1668)，作为斯特凡诺·德格利·安吉利的学生。然而，这种说法是有问题的。首先，格列高利在帕多瓦停留的时间只有1667-1668年。其次，格列高利在求积问题领域的首次著作《圆方形论》(Vera quadratura circuli, ellipseos and双曲线in sua propria specie inventa et demonstrata)的部分抄写本的存在，以及佛罗伦萨国家图书馆保存的一些信件，表明格列高利与意大利数学家之间的关系比人们想象的要复杂和多样。根据新的，尽管稀缺的，文本证据，我将提出一些关于格列高利可能在帕多瓦，罗马，或者佛罗伦萨遇到的学者和哲学家的猜想。
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2019.1678829
M. Segre
Niccolo Fontana (1499 or 1500–1557), nicknamed Tartaglia due to his stammer, is one of the most fascinating figures at the roots of early modern science. He is primarily famous for having solved th...
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Pub Date : 2020-01-02DOI: 10.1080/26375451.2020.1702670
Isobel Falconer
s from past meetings Workshop on Mathematical and Astronomical Practices in Pre-enlightenment Scotland and her European Networks 23–24 November 2018 University of St Andrews Alison Morrison-Low (National Museums of Scotland) Surviving scientific instruments from early modern Scotland: a survey When did instrument-making come to Scotland? In contrast to the rest of Europe, this activity appeared relatively late. Humphrey Cole was the first native-born English instrument maker, taught by immigrant Flemings in the last days of the Tudor dynasty. Itemsmade locally before the Restoration of the Stuarts in 1660 remain extremely unusual. The earliest signed instrument made in Scotland is now held by National Museums Scotland, having appeared in a London saleroom in 1972. It is signed by Robert Davenport, who had served his apprenticeship with the great Londonmaker Elias Allen, whowas commissioned byWilliamOughtred to make both Oughtred’s ‘Circles of Proportion’ (the earliest logarithmic calculating scale, which is on the reverse of this instrument) and the horizontal instrument, which used his form of stereographic projection. Davenport was working in Edinburgh by 1647, but it is not known for how long he stayed. This is the only instrument known with his signature, and was made for the latitude of Edinburgh. Of course, that is not to say that mathematical instruments or instruments used in natural philosophy were unknown in Scotland before this date: and this paper will discuss a number of these. Samuel Gessner (Lisbon) Thinking with instruments and the appropriation of logarithms on the Iberian Peninsula around 1630 Lord Napier’s tables and their explanation were actively publicized by the mathematical practitioners gravitating around Gresham college in London in the 1610s. In the spirit of that context, characterized by an acute interest for mathematical instruments, Gunter and Oughtred, a few years later, devised logarithmic scales to put on instruments. Both sought the expertise of the instrument maker Elias Allen to turn their ideas into brass objects. This paper focuses on a Jesuit who lectured on mathematics at the College of Santo Antão in Lisbon: Ignace Stafford. He elaborated two manuscripts in Castilian that touch upon logarithms in the 1630s. One is about trigonometry, the second is a practical arithmetic that systematically treats the various problems by Gunter’s and Oughtred’s logarithmic instruments. Stafford’s books represent evidence of the impressive velocity with which knowledge about logarithms and connected instruments spread to the other end of Europe and the readiness with which it has been absorbed into local treatise production. These exceptional sources prompt the question of the importance of instruments for new mathematical concepts to travel. In particular, they allow Volume 35 (2020) 95
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