Andrea Bréard

Andrea Bréard
Friedrich-Alexander-University of Erlangen-Nürnberg | FAU · Department of Classical World and Asian Cultures

Diplom (Mathematics & Computer Science, TU München), Master (History of Science, Fudan University), PhD (Philosophy, TU Berlin), PhD (Epistemology, Paris 7), Habilitation (History of Science, TU Berlin)

About

92
Publications
16,310
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113
Citations
Citations since 2017
31 Research Items
82 Citations
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Introduction
I am currently working on a French translation and commented edition of Li Shanlan's 李善蘭 (1811-1882) Duoji bilei 垛積比纇 from 1867, a deductively constructed collection of combinatorial identities and generalized arithmetic triangles (to be published in the series Bibliothèque Chinoise by Les Belles Lettres in Paris). Another major project of mine concerns the history of quantification in modern China. Research is conducted from a global perspective of political epistemology in collaboration with colleagues in France, Germany and China. Finally I am interested in connections between logic, mathematics and the Chinese language and currently working on the mathematician and sinologist Giovanni Vacca (1872-1953), my intellectual soulmate, so to say.
Additional affiliations
November 2017 - present
Université Paris-Saclay
Position
  • Professor (Full)
April 2017 - September 2017
Goethe-Universität Frankfurt am Main
Position
  • Professor (Full)
April 2014 - September 2014
Universität Heidelberg
Position
  • Professor
Description
  • Teaching seminars to students from the MATS (Master in Transcultural Studies) program and the Sinology Department.
Education
October 2005 - October 2008
Technische Universität Berlin
Field of study
  • History of Science
September 1994 - September 1997
Technische Universität Berlin
Field of study
  • Kommunikations- und Geschichtswissenschaften
September 1994 - September 1997
Paris Diderot University
Field of study
  • Epistémologie, Histoire des Sciences Exactes et des Institutions scientifiques

Publications

Publications (92)
Article
Attitudes towards diagrammatic reasoning and visualization in mathematics were seldom spelled out in texts from pre-modern China, although illustrations figure prominently in mathematical literature since the eleventh century. Taking the sums of finite series and their combinatorial interpretation as a case study, this article investigates the epis...
Article
Cet article publié dans un numéro spécial (Chance, destin et jeux de hasard en Chine) de la revue Études Chinoises porte sur le rôle des nombres dans les techniques de divination et les jeux de dominos en Chine à partir de la fin des Ming. Même si la quantification du hasard ne figurait pas explicitement parmi les sujets traités dans des textes mat...
Chapter
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Die Zahl im Titel dieses Beitrages mag im Hinblick auf das Leibniz-Jubiläum im Jahr 2016, dem 300. Todestag des Gründers der Akademie, als Lapsus erscheinen. Blicken wir aber einhundert Jahre zurück, so richtet sich unser Augenmerk auf eine Zeit, die durch eine große Vielfalt an Sprachprojekten besticht und in den Bereichen der Logik sowie der Spra...
Book
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The title of the book and its number of chapters is a pun on the canonical Nine Chapters on Mathematical Procedures (Jiu zhang suan shu 九章算術), compiled during the first century CE. The classic and its commentaries played an important scientific and political role in the mathematical endeavours of nineteenth- and twentieth-century mathematicians wor...
Article
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Numerous recent discoveries in China of ancient tombs have greatly increased our knowledge of ritual and religious practices. These discoveries include excavated oracle bones, bronze, jade, stone and pottery objects, and bamboo manuscripts dating from the twelfth to fourth century BCE. Inscribed upon these artifacts are a large number of records of...
Article
Chinese characteristics began to be defined in quantitative terms in the early twentieth century. This allowed comparisons and provided scientific answers in the search for the relative position of the Chinese in the historical evolution of human beings and the origins of mankind, thereby challenging earlier culturally defined notions of a Chinese...
Article
Analyse critique de : The Origins of Sciences in China / edited by Jiang Xiaoyuan. – Singapour : Springer & Shanghai Jiao Tong University Press, 2021. – x, 962 p. – (History of Science and Technology in China ; 1). – 319,93 €. – isbn 978-981-15-7854-0 (version électronique). The Studies of Heaven and Earth in Ancient China / edited by Jiang Xiaoyua...
Chapter
This chapter analyses Li Shanlan’s 李善蘭 (1811–1882) original attempt to disclose the Euclidean canon by adding an extra procedure for testing the primality of a number. Li is a particularly interesting figure since he worked and taught mathematics in a compartmentalized fashion: either in traditional algorithmic Chinese style or by adopting a syncre...
Chapter
This chapter is about the conflictual relations among pure and applied mathematical disciplines in the century from circa 1850 to 1950. It shows the historical variations associated with the ways in which boundaries were drawn in this period, and how, often under the influence of the political orientations of China in a global context, the focus up...
Chapter
This chapter relates to the seemingly most universal object of mathematical endeavours: the symbolic language of mathematics and, in relation to it, the individual mediators who established connections between discursive and formal modes of scientific discourse. Situated in China at the turn of the twentieth century, it describes the power-laden pr...
Chapter
This chapter suggests another theme that is both non-technical in nature and global-historically relevant: the institutional history of collecting numbers in late Qing imperial bureaucracy, in particular by China’s first central Statistical Bureau (Tongji ju 統計局) created in 1907, and the related changes that occurred in the conceptualization of num...
Chapter
This chapter uses the case of the ellipse as a new geometrical object introduced to China in the context of Aristotelian mechanics and Keplerian astronomy in order to analyse how authors in late imperial China, in particular before the introduction of differential and integral calculus, approached the rectification and quadrature of curves. It not...
Chapter
This chapter describes attempts to prove the rational foundations of Chinese cosmological and divinatory traditions: one, by Jiao Xun 焦循 (1763–1820), grounding the sequence of the divinatory hexagrams as described in the Classic of Changes (also known under its Chinese title Yijing 易經) in combinatorial theories; the other, by Yuan Shushan 袁樹珊 (1881...
Chapter
The last of the present Nine Chapters analyses the nationalist and ideological aspects of some twentieth-century self-assertive discourses that connect Chinese tradition and modernity with backwardness and progress in science. It shows what persists of China’s efforts to revive its scientific past today and problematizes the notion of “modernity” a...
Chapter
The first of the present Nine Chapters analyses the nationalist and ideological aspects of some nineteenth- and twentieth-century self-assertive discourses that connect Chinese tradition and modernity with backwardness and progress in science. These historiographic snapshots reveal different ways of instrumentalizing research on China’s mathematica...
Chapter
Moving from the linguistic to the discursive level, this chapter examines the changing modes of argumentation and analyses the ways in which the authority of these modes of argumentation was built upon both Chinese philosophical and foreign elements. Whether it is inductive proof, visual tools, or arguments by analogy in number-theoretical contexts...
Presentation
Full-text available
In diesem Vortrag zeichnete ich anschaulich nach, wie sich das Verhältnis sprachlicher Ästhetik zu sachlicher Abstraktion und algebraischen Formalismen in China entwickelte.
Chapter
This chapter analyzes late imperial understandings of objects and methods of statistics not only in their relation to the later development of modern statistics, but also by taking into account the coexistence of traditional modalities and imported institutions and practices at the end of the Qing. It uses administrative, methodological and mathema...
Chapter
In der Statistik, in dem Sinne wie sie in diesem Beitrag verstanden werden soll, geht es nicht allein um das logisch Rechenhafte und Operationelle, nicht nur darum, dass Zahlen als objektiv-rationale Objekte behandelt und gesammelt, als Routine oder Prosaik verstanden werden. Es geht um die Zahl als eine mobile gesellschaftliche Ware, eine Ware, di...
Chapter
Giuseppe Peano’s (1858–1932) longtime assistant in infinitesimal calculus at the University of Torino, Giovanni Vacca, played a decisive role in the so-called Leibniz Renaissance in Europe at the turn of the 20th century. Upon Peano’s advice, but also for his personal interest in natural and universal language schemes, logic, and mathematics, Vacca...
Presentation
Full-text available
Attitudes towards reasoning in mathematics were seldom spelled out explicitly in texts from early modern China. A historical shift nevertheless can be observed after the second wave of influx of Western modes of argumentation and proof during the second half of the 19th century. Taking Li Shanlan’s 李善蘭 (1811-1882) Comparable Categories of Discrete...
Presentation
Full-text available
Based on my work on the history of quantification in non-democratic regimes, my presentation given at the Digital Humanities Institute of the Ecole Polytechnique Fédérale de Lausanne (EPFL) took a critical historical approach to science-technology-state relations of the much debated social credit system in China.
Chapter
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In this essay, I go beyond China and beyond the field of mathematics itself in order to explore conceptual changes across disciplines, especially disciplines involving language. Such explorations, as well as the related philosophical issues, hinge on the very idea of what a mathematical concept is. There is no unique answer to this as one might exc...
Chapter
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The description of the relation between different mathematical traditions reveals a tension between individual creation and the dynamics of global knowledge circulations. By translating local practices of mathematical thought into the modern universal language of algebraic formulas, the question of the cultural relativity of mathematics becomes sup...
Article
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Dans son article « Euclide en Chine ou comment faire communiquer différentes cultures mathématiques ? », Andrea BRÉARD s’intéresse au destin singulier que les mathématiques ont connu en Chine durant les XVIIème et XVIIIème siècles. L’auteur développe son propos à travers le cas de la géométrie euclidienne, sa réception parmi les lettrés en Chine ;...
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After the Qing defeat to Japan in 1895, the latter came to be a major place of knowledge for those involved in reforming China. This chapter analyzes the careers of two individuals who each belonged to one of the two social groups involved in the modernization of statistics—a term whose multiple meanings at this particular historical juncture she d...
Presentation
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Ich interessiere mich in meinem Vortrag für die Fortsetzung der Sprachprojekte Leibniz’ – des logischen calculus ratiocinator und der characteristica universalis – im Werk des italienischen Mathematikers Giuseppe Peano (1858-1932), der sich explizit und detailliert auf die Werke Leibniz’ bezog. Ausschlaggebend war dabei die Veröffentlichung von Lou...
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Research
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Book proposal, accepted in the Heidelberg Studies in Transculturality book series.
Chapter
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Superstitious beliefs in auspicious and inauspicious numbers were traditionally based on cosmological correspondence systems and have increasingly become popular by relying purely on linguistic puns, where homophones of numerals replace the symbolic meaning of number words and graphs.
Chapter
Mathematics Education in China Andrea Bréard The first section of this chapter focuses on the period covering the late sixteenth to the early twentieth century in China, from the beginning of the Jesuit influence to the educational reforms, ending the more than 1,000-year-old traditional state examinations and introducing a modern school system bas...
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Versified mathematical algorithms and problems make their appearance in China around the end of the Song dynasty (eleventh century) and are widely spread among the sources of the Ming (1368–1644) and the Qing (1644–1911) dynasties.
Chapter
First of all, this chapter describes the central role played by Yoshida Mitsuyoshi's Jinkōki (1627) as an elementary textbook, written in vernacular language and widely read throughout the Edo period. It then deals with the specific context of private schools in the main cities and the way mathematicians used to communicate and compete with each ot...
Chapter
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Combinatorial practices in China go back to high antiquity, when divinatory techniques relied on configurations of broken and unbroken lines. The Yijing or I Ching (Book of Change), compiled under the Zhou dynasty, has transmitted these practices up to the present time and has been a widely commented upon and read source. But combinatorial practice...
Article
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Die Beschäftigung mit der wissenschaftlichen Kultur Chinas ist eine wahre Herausforderung an den Geist des im „Westen“ trainierten Mathematikers. Misst man die Art und Weise, wie in China mathematische Aussagen formuliert wurden gemäß den Normen moderner wissenschaftlicher Praxis, so muss man feststellen, dass nichts unseren Standards gleicht. Dara...
Conference Paper
Full-text available
Traditionally, the knowledge of mathematics should have been exclusive to the privileged class which gained the knowledge primarily through family connections or literati circles. A short third century canonical text, the Sea Island Mathematical Classic provides such theoretical knowledge privileged by the upper class written in the form of mathema...
Book
Dans le cadre de l' « Année Internationale de la Chimie 2011 », un colloque international sur « La chimie au lendemain des révolutions - Gay-Lussac et l'après-Lavoisier » s'est tenu les 29 et 30 septembre 2011 à l'École polytechnique. Nous y souhaitions réexaminer l'oeuvre de Gay-Lussac et celle de ses contemporains chimistes en les resituant dans...
Article
Full-text available
As a historian of mathematics in China, I am particularly interested in the cultural contexts out of which mathematical procedures grew to solve combinatorial questions: logic, grammar, lottery, games of chance or strategy and interrupted games all were playgrounds of combinatorial practice to explore experimentally and theoretically the number of...
Article
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My contribution pp. 265-267 is a review of Victor J. KATZ (ed.), The Mathematics of Egypt, Mesopotamia, China, India and Islam. Princeton, Princeton University Press, 2007.
Chapter
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Since the Song dynasty the official bibliographic monographs referenced an independent category of works generally translated as “encyclopedias” (leishu類書, lit. “books topically arranged”), a classification developed by the Confucianist Zheng Qiao 鄭樵 (1104–1162). The leishu sections included a heterogeneous range of collections of examination liter...
Chapter
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Andrea Bréard apporte un éclairage complémentaire aux pratiques lettrées au Japon et en Chine en offrant une introduction à une catégorie d’écrits peu étudiés jusque là en France, à savoir celle des encyclopédies « des dix mille trésors » produites au xvie siècle, sous la dynastie des Ming. Ces encyclopédies, regroupant des connaissances de base su...
Article
从19世纪末期至20世纪初期,统计学在中国完成了从传入到发展的第一个进程。在近半个世纪的时间里,中国统计学的发展浓缩了西方统计学近两百年的发展历程,较之其他的西学知识在近代中国的传播和发展,统计学的历史则表现出了其自身的独特性,这种发展受到当时的社会政治、经济、文化等方面的影响甚大。这是由当时中国的社会背景以及统计学这门学科知识的特殊性质所决定的。
Article
Full-text available
Aujourd'hui, le domaine mathématique que l'on appelle " combinatoire " est étroitement lié à la théorie des nombres et à la théorie des graphes. Dans le passé, c'est avant tout un intérêt pour les diverses combinaisons d'un nombre fini d'objets, suivant certaines règles et afin de créer avec eux les arrangements les plus variés, qui a inspiré le dé...
Conference Paper
Full-text available
L'écriture (ou plutôt la re-écriture) des algorithmes mathématiques sous forme versifiée apparaît en Chine vers la fin des Song (XI e siècle), et est largement répandue dans les sources à partir des Ming (1368-1644). Les manuels ou chapitres mathématiques contenant des vers et rimes présentent de nombreux points communs : tout d'abord, ils font tou...
Article
Aujourd’hui, le domaine mathématique que l’on appelle « combinatoire » est étroitement lié à la théorie des nombres et à la théorie des graphes. Dans le passé, c’est avant tout un intérêt pour les diverses combinaisons d’un nombre fini d’objets, suivant certaines règles et afin de créer avec eux les arrangements les plus variés, qui a inspiré le d...
Conference Paper
Mathematical writings in China relied entirely on the algorithmic mode to express sequences of operations, to justify the correctness of these, and to bring mathematical objects in relation one to another. In this paper, I shall use one example to show how the structural elements in an algorithm convey a mathematical meaning and can be interpreted...
Conference Paper
Full-text available
A la fin de la période impériale, le gouvernement chinois visait par des réformes politiques et une remodélisation du système administratif et éducatif à transformer les sujets de l’empereur en citoyens d’une monarchie constitutionnelle. Dans le cadre de ce programme de réformes, un premier Bureau de statistique (Tongji ju 統計局) central a été fondé...
Chapter
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Article
Cet article représente une réflexion personnelle sur des expériences d’enseignement de l’histoire des mathématiques dans des aires géographiques et culturelles distinctes. Il n’a pas été écrit avec l’intention de montrer ou expliquer des différences internationales en termes de performances ou compétences mathématiques. Ce sujet a fait couler beauc...
Chapter
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In pursuing the roots of a subject back to endeavours in the Ancient World modern writ-ings on statistics in China presume that the very concept of statistics has remained un-changed. They thus identify mathematical procedures in the 7 th century compilation, the Ten Books of Mathematical Classics (Suan jing shi shu as being foundational to the dev...
Article
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This is a book on the ambiguous fate of a literary source from traditional China. The so-called pulu (literally, treatises and lists) are monographic texts on one or a group of material objects coming from either the natural or the artificial world, as for example chrysanthemums, ink stones, tea, tobacco, or such techniques as lacquering or goldfis...
Article
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The introduction of statistics in late Imperial China took place in the context of administrative and educational reforms, which followed mainly Meiji Japan’s political model after the Chinese defeat in the first Sino Japanese War. Constitutional and educational reform provided a territory to implant statistical institutions in the capital and the p...
Article
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In this essay, I first discuss Qing statistical institutions as well as late Qing innovations. I then describe the Statistical Department of the Customs. I also explore why the Statistical Department would initially have little impact on other Chinese government bureaucracies. It was only following the great crisis of the Boxer Rebellion in 1900 an...
Article
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This paper tries to analyze the origins and the development of nomenclature and classification schemes between 1870 and 1911 in Chinese foreign trade statistics as established by the statistical bureaus of the Imperial Maritime Customs under foreign management and the purely Chinese staffed statistical office of the Board of Agriculture, Industry a...
Article
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This paper presents the major accomplishments of research over the past quarter century in the field of Chinese mathematics and its history. We begin with a brief overview of the progress of our knowledge of that history, and the major figures who contributed the fundamentals early works prior to 1975, and then examine more carefully the achievemen...
Chapter
Full-text available
In a seventh-century commentary on an astronomical problem from the Mathematical Classic in Continuation of Antiquity (Ji gu suan jing) a problem of pursuit is borrowed from the Nine Chapters on Mathematical Procedures (Jiu zhang suan shu). Similar couples of problems can be found in an Indian commentary to the ryabhaīya from the seventh century, a...
Chapter
Zhu Shijie (soprannominato Hanqing, pseudonimo Songting) è rappresentato dalla storiografia della matematica in Cina come uno dei personaggi maggiormente ignorati, benché si tratti, come oggi sappiamo, di una delle menti matematiche più brillanti. Vissuto nel XIII-XIV sec., egli non è menzionato né negli annali ufficiali della dinastia Yuan (1279-1...
Book
Die vorliegende Reise durch fast zwei Jahrtausende chinesischen mathematischen Denkens, erzählt anhand eines ausgewählten Begriffs ("Reihen"), stellt einen bedeutenden Beitrag zur Erforschung der Mathematikgeschichte und zu den Fragen des Umgangs mit Texten hohen Alters, der Universalität von Objekten und den Besonderheiten chinesischer Argumentati...
Article
Shen Gua’s treatment of mathematics in his Brush talks from the dream pool (Meng xi bi tan, 11th century) is nearly unique among the traditions of Chinese Song dynasty mathematics transmitted to us in its distinctly different formulation of diverse algorithms. It might seem surprising, therefore, that commentators and historians of science frequent...

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Projects (5)
Project
In this project I focus upon Giuseppe Peano’s (1858–1932) and Giovanni Vacca’s (1872-1953) attempts of translation between mathematical formulas and Chinese text, either via simplified Latin or via mathematical logic. It sheds light on early 20th century logical and at the same time philological approaches to the Chinese language and to mathematical language more generally.
Project
Li Shanlan李善蘭 (1811-1882), lettré et mathématicien de la fin des Qing, se situe par sa pratique scientifique au carrefour des mathématiques occidentales et des mathématiques traditionnelles. Il était traducteur d’ouvrages en langue anglaise sur la géométrie euclidienne et l’analyse, il enseignait l’algèbre au Tongwenguan à Pékin de deux façons : symbolique d’un côté, et en suivant les conventions de la méthode de l’inconnue céleste de la dynastie des Yuan de l’autre. Li rédigeait des ouvrages mathématiques aussi bien en continuation des thèmes de la tradition algorithmique chinoise que sur des sujets « modernes » comme la théorie des nombres premiers, les fonctions elliptiques, les logarithmes, etc. Les Catégories analogues d'accumulations discrètes (Duoji bilei 垛積比纇), desquelles je prépare une édition et traduction commentée pour les Belles Lettres, est particulièrement intéressant sous ce double aspect du travail mathématique en combinatoire. Rédigé en langue naturelle, l’ouvrage ne contient aucune formule algébrique, le discours est systématiquement construit en lien avec des « diagrammes » (tu 圖), des « tables » (biao 表) numériques (les triangles arithmétiques), des « explications » (jie 解) indiquant la construction de la suite des nombres dans les cellules des tables, et des « méthodes » (fa 法) pour calculer la somme des diagonales. Li énonce un grand nombre de relations de la théorie des nombres, mais ne donne aucun argument explicite comment il a obtenu ses résultats. Le langage est extrêmement stéréotypé, avec souvent les mêmes expressions pour indiquer le passage des cas particuliers à la procédure générale. Tout l’intérêt de l’ouvrage repose dans sa structure et dans son langage technique concis qui fait implicitement référence à un schéma inductif d’argumentation.