Nathan Sidoli

Bio: Nathan Sidoli is an academic researcher from Waseda University. The author has contributed to research in topics: Greek mathematics & Ancient Greek. The author has an hindex of 11, co-authored 24 publications receiving 324 citations. Previous affiliations of Nathan Sidoli include University of Toronto & Simon Fraser University.

Visualisation and proof: a brief survey of philosophical perspectives

Abstract: The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification.

Aristarchus's on the sizes and distances of the sun and the moon: Greek and Arabic texts

Abstract: In the 1920s, T. L. Heath pointed out that historians of mathematics have "given too little attention to Aristarchus" (Heath 1921, vol. 2, 1). This is still true today. The Greek text of Aristarchus's On the Sizes and Distances of the Sun and the Moon has received little attention; the Arabic editions virtually none.1 For these reasons, much of what this text has to tell us about ancient and medieval mathematics and the mathematical sciences has gone unnoticed. When one considers that many of Aristarchus's arguments are obscure and much of his mathematics cumbersome, the persistent interest in this text during the medieval and early modern periods is remarkable. It was edited and studied by Arabic scholars long after all of its mathematical methods and most of its astronomical results had become otiose. Copies of the Greek manuscripts were still being made by Latin scholars in the 17th century, well after the ascent of printed text.2 The work begins with a series of hypotheses that are at once crude and contradictory and yet refreshingly bold. From these, by great labor, Aristarchus derives a few precise statements about objects far outside our common purview, displaying an incisive ability with theoretical modeling. The text is a fine example of that style of Greek mathematics which produces, from seemingly intractable quagmires, results that are simple and clean. All of these features must have delighted the many generations of mathematicians who studied On Sizes. But perhaps they were struck by something simpler than the detailed arguments and the actual results. Perhaps they were struck by the work's fundamental, unspoken claim. On Sizes implies, unequivocally, that the world is mathematical; not just in a vague qualitative way, but in a precise quantitative way. It demonstrates that by starting from a few simple and readily obtainable statements one can, through the

The role of geometrical construction in Theodosius's Spherics

Abstract: This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius’s Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams.

Research on Ancient Greek Mathematical Sciences, 1998-2012

Abstract: This survey deals with research in ancient Greek mathematics and, to a lesser extent, mathematical sciences in the long first decade of the 21st century. It is modeled on the two foregoing surveys by J.L. Berggren and K. Saito and gives my personal appraisal of the most important work and trends of the last years, with no attempt to be exhaustive.

A Complete Bibliography of Publications in Isis, 2000{2009

Abstract: accademiche [38]. Ada [45]. Adrian [45]. African [56]. Age [39, 49, 61]. Al [23]. Al-Rawi [23]. Aldous [68]. Alex [15]. Allure [46]. America [60, 66]. American [49, 69, 61, 52]. ancienne [25]. Andreas [28]. Angela [42]. Animals [16]. Ann [26]. Anna [19, 47]. Annotated [46]. Annotations [28]. Anti [37]. Anti-Copernican [37]. Antibiotic [64]. Anxiety [51]. Apocalyptic [61]. Archaeology [26]. Ark [36]. Artisan [32]. Asylum [48]. Atri [54]. Audra [65]. Australia [41]. Authorship [15]. Axelle [29].

An Examination of Research Methods in Mathematics Education (1995-2005):

Abstract: This mixed methods examination of 710 research articles in mathematics education published in six prominent educational journals during the period 1995-2005 finds that 50% of the studies used qualitative methods only, 21% used quantitative methods only, and 29% mixed qualitative and quantitative methods in various ways. Although the number of mixed methods articles show some variation year to year and journal to journal, there is no discernible trend in the aggregate across this time period for the collection of journals studied. Issues explored include defining research categories and subsequently categorizing studies, balance and dominance between quantitative and qualitative strands, and integration within conclusions.

Scale, Space and Canon in Ancient Literary Culture

Abstract: Greek culture matters because its unique pluralistic debate shaped modern discourses. This ground-breaking book explains this feature by retelling the history of ancient literary culture through the lenses of canon, space and scale. It proceeds from the invention of the performative 'author' in the archaic symposium through the 'polis of letters' enabled by Athenian democracy and into the Hellenistic era, where one's space mattered and culture became bifurcated between Athens and Alexandria. This duality was reconfigured into an eclectic variety consumed by Roman patrons and predicated on scale, with about a thousand authors active at any given moment. As patronage dried up in the third century CE, scale collapsed and literary culture was reduced to the teaching of a narrower field of authors, paving the way for the Middle Ages. The result is a new history of ancient culture which is sociological, quantitative, and all-encompassing, cutting through eras and genres.