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In this paper, we focus on the launch of the Great Soviet Encyclopedia, which was first published in 1925. We present the context of the launch and explain why it was closely connected to the period of the New Economic Policy. In the last section, we examine four articles about randomness and probability included in the first volumes of the encyclopedia in order to illustrate some debates from within the scientific scene in the USSR during the 1920s. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the origins of Emile Borel's developing interest in probability around 1905. This resulted from new findings in his research on continued fraction, but it also cannot be separated from the discovery of new applications for the mathematics of randomness (such as biology or economics) and of their importance as a life-changing tool for the citizen. In particular, we underline the role of a paper published by Vito Volterra in Borel's Revue du Mois. [ABSTRACT FROM AUTHOR]

During the first 3 years of the existence of the Journal für die reine und angewandte Mathematik (1826–1828), a now unknown mathematician named Louis Olivier contributed 12 articles covering a broad range of contemporary mathematics. Apart from a single ‘faulty’ result, none of these works have received much interest from historians of mathematics. Nevertheless, Olivier’s mathematical production invites historical analysis as it provides the historian with a perspective on the mathematics of the 1820s that is perhaps more typical than the works of the now famous mathematicians. Although he contributed no great new insights into geometry, algebra, or analysis, Olivier dealt with all these topics, in particular with discussions that were up in his time. His publications were not so much aimed at presenting new research but rather with disseminating the established knowledge. As such, they fitted the ambitions that A. L. Crelle (1780–1855) had set for his new journal in 1826. After two productive years with the journal, Olivier faded into complete oblivion soon after 1828. The available sources offer no reason for this. However, Olivier’s publications and the development of the journal during its initial years suggest an explanation why his contributions stopped. [ABSTRACT FROM AUTHOR]

As a reaction to the changed political landscape in Scandinavia following the dissolution of the union between Norway and Sweden in 1905, the prominent Swedish mathematician Gösta Mittag- Leffler extended 'a brotherly hand,' calling for Scandinavian colleagues to meet for a congress of mathematicians in Stockholm in 1909. This event became the first in a series of biannual meetings which proved to be an important institution for Scandinavian mathematics. During the first decades after 1909, the congresses would form and consolidate themselves through the construction of a new Scandinavian identity for mathematicians which developed alongside and in relation to both international and national contexts and developments. In this paper, we shall demonstrate that these meetings served a complex set of agendas at the individual, national, and international level. In particular, they reflect a changing conception of cooperation in science for mutual cultural gain combined with a flexible institutionalisation that allowed the Scandinavian mathematicians to use the congresses for various diplomatic ambitions. We base our analyses of the Scandinavian Congresses of Mathematics on the notion of a shared 'conational' identity developed adjacent to national identities. We then analyse the formation, consolidation, delineation, and reflections of this institution in order to demonstrate how the efforts to unite Scandinavian mathematicians were contingent on and influenced by simultaneous currents of internationalisation and shared history, culture, and language in the Scandinavian region. [ABSTRACT FROM AUTHOR]

This paper is devoted to an outline of certain aspects of international scientific cooperation and exchange between Eastern and Western European countries from 1950 to 1989, with an emphasis on mathematics, biochemistry and neuroscience. [ABSTRACT FROM AUTHOR]

In 1857, a Statistical Society was founded in the Netherlands. Within this society, statistics was considered a systematic, quantitative, and qualitative description of society. In the course of time, the society attracted a wide and diverse membership, although the number of physicians on its rolls was low. The society itself was dynamic, discussing statistical and economic topics at its annual meetings, working to compile a ‘General Statistics of the Netherlands’, and publishing a yearbook. Although the lack of well-organised, official, state-generated statistics played a role in the foundation and continued existence of the Statistical Society, this does not seem reason enough to explain why the society changed its name and stopped being engaged in statistical matters when a central official statistics organisation was finally created in the Netherlands in 1892. Explaining this transformation is important, as the abolition of that aspect of the society was crucial to the development of statistics in the Netherlands. In this paper, I sketch the foundation, history, and the demise of the Dutch Statistical Society and compare some of its characteristics with the English Royal Statistical Society. Through this examination, I try to answer the question why this 19th-century statistical society abandoned statistics. [ABSTRACT FROM AUTHOR]

In 1768, Kant published a short essay in which he inquired into the possibility of determining the directionality of space. Kant's central argument invokes the strategy that if one were to demonstrate directionality, then the relational view of space that Leibniz propounded would be refuted. This paper has been considered a major turning point in Kant's philosophical development towards his critical philosophy of transcendental idealism. I demonstrate that in this study, Kant came very close to the modern concept of symmetry. His novel construction of incongruent counterpart ( inkongruentes Gegenstück) contains elements essential to the modern notion of symmetry. However, Kant does not consider the incongruent counterparts, which he designates as ‘Right’ and ‘Left’, symmetric; rather, he holds the French encyclopaedist view that symmetry is a kind of balance. This study convinced Kant that the solution to the problem of the nature of space lies not in mathematics but in metaphysics. He was wrong in this conclusion, at least with respect to symmetry. The solution was found within the framework of mathematics, that is, solid geometry. In 1794, Legendre recast the traditional encyclopaedist concept of symmetry by calling a certain property of polyhedra symmetrical. The view of Kant is contrasted with that of Legendre by comparing their usages of mirror image as an aid for understanding. While in both cases mirror images are not considered illusions—perhaps for the first time in the history of mirror reflections—the differences are substantial, highlighting the limitation of Kant's position and the great potential of Legendre's new concept of symmetry. [ABSTRACT FROM AUTHOR]

The present paper offers strong evidence that there was a particularly advanced, for the era, sense and application of geometry in the prehistoric civilization of the island of Thera (Santorini), Greece, ca. 1650 BC. First, by applying an original method, it is demonstrated that specific shapes, depicted on so far unpublished wall paintings initially decorating the third floor of Xeste 3, correspond to advanced geometric configurations with remarkable accuracy. Thus, it is shown that there are configurations corresponding to linear spiral prototypes, others matching elliptical prototypes and sets of points lying on isogonal lines that are radii of regular polygons with 48, 32, and 24 angles. Subsequently, it is shown that the use of geometric archetypes for drawing played a prominent role in the Late Bronze Age Thera civilization. In fact, it is demonstrated that celebrated wall paintings have border lines that impressively match a limited number of linear (Archimedes’) spirals, hyperbolas, and ellipses in a piecewise manner. This practically excludes the probability that these wall paintings were drawn by freehand, while, on the contrary, it strongly suggests that they were mainly drawn by means of geometric stencils. [ABSTRACT FROM AUTHOR]

Heron's Dioptra 35 is the unique witness of an ancient mathematical procedure for finding the great arc distance between two cities using methods of ancient spherical astronomy and simultaneous observations of a lunar eclipse. This paper provides a new study of the text, with mathematical and historical commentary. I argue that Heron's account is a summary of some longer work of mathematical astronomy or geography, which made extensive use of the analemma, an ancient model of the celestial sphere. Heron's text can be used to show the utility of the analemma model, both as a theoretical device and as a computational tool. [ABSTRACT FROM AUTHOR]

Duhem considered himself as the upholder of a 'third way' to Thermodynamics. His generalized Mechanics/Thermodynamics aimed at encompassing all kinds of transformations, from spatial changes to the change of physical qualities. From 1886 until 1896 he undertook a demanding design for the unification of physics. He translated Thermodynamics into the language of Analytical Mechanics, and conversely founded Mechanics on the principles of Thermodynamics. Step by step he widened the mathematical and conceptual structure of Analytic Mechanics, in order to hold together 'local motion,' thermal phenomena, electromagnetic phenomena, and many kinds of irreversible transformations. At the same time, he tried to recast methods and targets of physics: from the reductionist tradition of Mechanics he let a new interest in the complexity of the natural world emerge. Modern science had had to fight against the old physics of qualities, in order to supplant it: the complexity of the physical world was set aside, and replaced by a simplified geometrical world. Duhem endeavoured to retrieve and take that neglected complexity into the wide boundaries of a generalized Mechanics-Thermodynamics. He aimed at widening the scope of physics: the new physics could not confine itself to ' local motion' but had to describe what Duhem labelled ' motions of modification.' [ABSTRACT FROM AUTHOR]

The Norwegian government created the Abel Prize in Mathematics in 2002 in memory of mathematician Niels Henrik Abel (1802-1829). The aim was to establish the annual Abel Prize as the world's leading prize in mathematics. The creation of the prize was the result of a short and successful campaign in the spring and summer of 2001, which presented the prize as 'the missing Nobel Prize in mathematics.' The prize was very well received, both by the international mathematical community and Norwegian politicians. Sweden's Nobel Foundation, however, found repeated references to the new prize as 'a Nobel in mathematics' to be quite inappropriate. This article focuses on how the prize was successfully established in Norway, a country considered by some to be at the mathematical periphery, and to what extent the Abel Prize has been able to live up to the high expectations during its first 10 years. [ABSTRACT FROM AUTHOR]

During the 17th century, important conventions for the visual representation of the Earth as a whole were established by writers of Theories of the Earth. This essay examines how the emergence of visual representations contributed to the establishment of a new print tradition of multicontextual discourse and critical debate. Four vignettes contrast varying uses of global depictions: the incidental global depictions and mathematical vision of Johannes Kepler; the cosmogonic sections and chemical vision of Robert Fludd; the geogonic sections and mechanical vision of René Descartes; and the global views and classical vision of Thomas Burnet. The continuities of visual conventions and the contrasts of disciplinary perspectives and local contexts observed in these vignettes conforms well to the characterization of Theories of the Earth as an interdisciplinary print tradition. [ABSTRACT FROM AUTHOR]

Richard Yeo, Science in the Public Sphere: Natural Knowledge in British Culture 1800–1860, reviewed by Peter C. Kjærgaard László Kovács, Eugene P. Wigner and his Hungarian Teachers, reviewed by Rajinder Singh C. D. Andriesse, Huygens. The Man Behind the Principle, reviewed by Fokko Jan Dijksterhuis Jöran Friberg, Unexpected Links Between Egypt- ian and Babylonian Mathematics, reviewed by Micah Ross Karine Chemla and Guo Shuchun, Les neuf chapitres: Le Classique mathématique de la Chine ancienne et ses commentaires. Édition critique bilingue traduite, présentée et annotée reviewd by Donald B. Wagner Sabine Rommevaux, Clavius. Une clé pour Euclide au XVIe siècle, reviewed by Paolo Palmieri Herbert Hunziker (ed.), Der jugendlichen Einstein und Aarau, reviewed by Helge Kragh Thomas K. Simpson, Figures of Thought: A Literary Appreciation of Maxwell’s Treatise on Electricity and Magnetism, reviewed by Bruce J. Hunt Klaus Hentschel, Die Mentalität deutscher Physiker in der frühen Nachkriegszeit, reviewed by Christian Forstner Sven Kinas, Adolf Butenandt (1903–1995) und seine Schule, Marie Louise Thomsen I. Grattan-Guinness (ed.), Landmark Writings in Western Mathematics 1640–1940, reviewed by Adrian Rice H. L. L. Busard, Campanus of Novara and Euclid’s Elements, reviewed by Jens Høyrup Andrew Brown, J. D. Bernal: The Sage of Science, reviewed by Henrik Knudsen David Cahan (ed.), From Natural Philosophy to the Sciences: Writing the History of Nineteenth-Century Science, reviewed by Peter C. Kjærgaard Aant Elzinga, Einstein’s Nobel Prize. A Glimpse Behind Closed Doors, reviewed by Henry Nielsen William R. Shea, Designing Experiments & Games of Chance: The Unconventional Science of Blaise Pascal, reviewed by Giora Hon Elisabeth R. Neswald, Thermodynamik als kultureller Kampfplatz. Zur Faszinationsgeschichte der Entropie 1850–1915, Helge Kragh [ABSTRACT FROM AUTHOR]

Francesco Maurolico wrote quite a number of pages about music, which were transcribed and edited by the author in Maurolico Opera Mathematica ( ). Here, in part I, his main results are presented and also their differences compared with the classical tradition of the mathematical theory of music. These results are a new proof of the number of commas in the tone, the theory of ‘ictus’, and a new notation for the composition of proportions. This is followed, in part II, by an explanation of how the original corpus of these folios was put together. Finally, part III discusses the complex puzzle of the manuscripts (one still extant, another probably lost, ...) and of their possible connections with the 1575 edition of a part of the corpus. Possible scenarios of the story of the manuscripts and probable interventions of the Jesuits on this edition are described. [ABSTRACT FROM AUTHOR]

Michal Kokowski, Copernicus’s Originality: Towards Integration of Contemporary Copernican Studies (Warsaw: Wydawnictwa Ihn Pan, 2004). 314 pp. pb. ISBN 83-86062-27-4. Sharon E. Kingsland, The Evolution of American Ecology 1890–2000 (Baltimore: Johns Hopkins University Press, 2005). 313 pp. hc. $50. ISBN 0-8018-8171-4. Graeme J.N. Gooday. The Morals of Measurement: Accuracy, Irony, and Trust in Late Victorian Electrical Practice (Cambridge: Cambridge University Press, 2004). xxv, 285 pp. hc. £55. ISBN 0-521-43098. Joan Vernet; Ramon Parés (eds.), La Ciència en la Història del Països Catalans. Vol. 1. Dels Àrabs al Renaixement (Valencia: University of Valencia, 2004). 630 pp. hc. €50. ISBN 84-370- 6047-8. Giuliano Pancaldi, Volta. Science and Culture in the Age of Enlightenment (Princeton and Oxford: Princeton University Press, 2003). 381 pp. hc. £32.50. ISBN 0-691-09685-6. Wolfgang Lefèvre; Jürgen Renn; Urs Schoepfin (eds.), The Power of Images in Early Modern Science (Basel: Birkhäuser Verlag, 2003). 320 pp. pb. CHF 184, € 118. ISBN 3-7643-2434-1. Olivier Darrigol, Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl (Oxford: Oxford University Press, 2005). 356 pp. hc. L35.00. ISBN 0-19-856843-6. Ad Meskens, Joannes della Faille s.j.: Mathematics, Modesty and Missed Opportunities (Brussel: Institut Historique Belge de Rome, 2005). 175 pp. hc. ISBN 90-74461-53-0. Aant Elzinga; Torgny Nordin; David Turner; Urban Wråkberg (eds.), Antarctic Challenges. Historical and Current Perspectives on Otto Nordenskjöld’s Antartic Expedition 1901–1903 (Göteborg: Royal Society of Arts and Sciences, 2004). 330 pp. hc. $93. ISBN 91-85252-64-6. Klaus-Heinrich Peters, Schönheit, Exaktheit, Wahrheit: Der Zusammenhang von Mathematik und Physik am Beispiel der Geschichte der Distributionen (Berlin: GNT-Verlag, 2005). 272 pp. pb. € 32.00. ISBN 3-928186-74-4. [ABSTRACT FROM AUTHOR]

Johannes Kepler's system of mathematical archetypes played a primary role in his physical cosmology. Identified as the geometrical models making up the metaphysical blueprint of the material world, Kepler's archetypes underlay every aspect of his world picture. Despite their importance, however, it has remained unclear how Kepler conceived of the archetypes in corporeal terms, that is, how he saw archetypes as being embodied in the form of material phenomena. Kepler's solution, I suggest, is an efficient cause, a facultas animalis, or animate faculty, pervading both the celestial and the terrestrial realms. In addition to its ability to realise the archetypes in their physical form, the animate faculty allowed Kepler to account for heavenly and earthly occurrences in terms of the same geometrical principles. Faraway phenomena such as comets and new stars could thus be seen as essentially comparable to more accessible curiosities on the Earth. [ABSTRACT FROM AUTHOR]

The Saros cycle of 223 synodic months played an important role in Late Babylonian astronomy. It was used to predict the dates of future eclipse possibilities together with the times of those eclipses and underpinned the development of mathematical lunar theories. The excess length of the Saros over a whole number of days varies due to solar and lunar anomaly between about 6 and 9 h. We here investigate two functions which model the length of the Saros found in Babylonian sources: a simple zigzag function with an 18-year period presented on the tablet BM 45861 and a function which varies with the month of the year constructed from rules found on the important procedure text TU 11. These functions are shown to model nature very well and to be closely related. We further conclude that these functions are the likely source of the Saros lengths used to calculate the times of predicted eclipses and were probably known by at latest the mid-sixth-century BC. [ABSTRACT FROM AUTHOR]

Discusses the significance of the book "The Statistical Mind in a Pre-Statistical Era: The Netherlands 1750-1850" and shows how the case study provides insight into the world of statistics of that time. Dutch interaction with foreign developments; Approaches to statistics that continued to co-exist in the Netherlands after its liberation from French occupation in 1813; Main parts of statistical description of the Netherlands according to Simon Vissering, professor of statistics.

Discusses the views of different philosophers on instrumentalism and realism. Information on how the late Karl R. Popper introduced the notion of instrumentalism; Discussion on how the epistemology of astronomical theories emerged as a problem for Greek philosophers; How the primeval harmony of physics and mathematical astronomy ended.