Mathematical Cultures: The London Meetings 2012-2014 PDF
Preview Mathematical Cultures: The London Meetings 2012-2014
Trends in the History of Science Brendan Larvor Editor Mathematical Cultures The London Meetings 2012–2014 Trends in the History of Science Trends in the History of Science is a series devoted to the publication of volumes arising from workshops and conferences in all areas of current research in the history of science, primarily with a focus on the history of mathematics, physics, and their applications. Its aim is to make current developments available to the community as rapidly as possible without compromising quality, and to archive thosedevelopmentsforreferencepurposes.Proposalsforvolumescanbesubmitted using the online book project submission form at our website www.birkhauser- science.com. More information about this series at http://www.springer.com/series/11668 Brendan Larvor Editor Mathematical Cultures – The London Meetings 2012 2014 Editor Brendan Larvor Schoolof Humanities University of Hertfordshire Hatfield,Hertfordshire UK ISSN 2297-2951 ISSN 2297-296X (electronic) Trends inthe History of Science ISBN978-3-319-28580-1 ISBN978-3-319-28582-5 (eBook) DOI 10.1007/978-3-319-28582-5 LibraryofCongressControlNumber:2016934201 ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisbookispublishedunderthetradenameBirkhäuser TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland (www.birkhauser-science.com) Contents Editorial Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Brendan Larvor Part I First Meeting: Varieties Understanding the Cultural Construction of School Mathematics. . . . . 9 Paul Andrews Envisioning Transformations—The Practice of Topology. . . . . . . . . . . 25 Silvia De Toffoli and Valeria Giardino Creative Discomfort: The Culture of the Gelfand Seminar at Moscow University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Slava Gerovitch Mathematical Culture and Mathematics Education in Hungary in the XXth Century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Katalin Gosztonyi On the Emergence of a New Mathematical Object: An Ethnography of a Duality Transform . . . . . . . . . . . . . . . . . . . . . . 91 Stav Kaufman What Are We Like …. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Snezana Lawrence Mathematics as a Social Differentiating Factor: Men of Letters, Politicians and Engineers in Brazil Through the Nineteenth Century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Rogério Monteiro de Siqueira “The End of Proof”? The Integration of Different Mathematical Cultures as Experimental Mathematics Comes of Age. . . . . . . . . . . . . 139 Henrik Kragh Sørensen Part II Second Meeting: Values Diversity in Proof Appraisal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Matthew Inglis and Andrew Aberdein v vi Contents What Would the Mathematics Curriculum Look Like if Instead of Concepts and Techniques, Values Were the Focus?. . . . . . . . . . . . . 181 Alan J. Bishop Mathematics and Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Paul Ernest Purity as a Value in the German-Speaking Area. . . . . . . . . . . . . . . . . 215 José Ferreirós Values in Caring for Proof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 John Mason and Gila Hanna An Empirical Approach to the Mathematical Values of Problem Choice and Argumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Mikkel Willum Johansen and Morten Misfeldt The Notion of Fit as a Mathematical Value. . . . . . . . . . . . . . . . . . . . . 271 Manya Raman-Sundström Mathematical Pull. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Colin J. Rittberg Part III Third Meeting: Interfaces Mathematics and First Nations in Western Canada: From Cultural Destruction to a Re-Awakening of Mathematical Reflections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Tom Archibald and Veselin Jungic Remunerative Combinatorics: Mathematicians and Their Sponsors in the Mid-Twentieth Century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Michael J. Barany Calling a Spade a Spade: Mathematics in the New Pattern of Division of Labour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 Alexandre V. Borovik Mathematics and Mathematical Cultures in Fiction: The Case of Catherine Shaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Tony Mann Morality and Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Madeline Muntersbjorn The Great Gibberish—Mathematics in Western Popular Culture. . . . . 409 Markus Pantsar Is Mathematics an Issue of General Education? . . . . . . . . . . . . . . . . . 439 Emil Simeonov Contributors Andrew Aberdein School of Arts and Communication, Florida Institute of Technology, Melbourne, USA Paul Andrews Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden Tom Archibald Department of Mathematics, Simon Fraser University, Burnaby, Canada MichaelJ.Barany DepartmentofHistory,PrincetonUniversity,Princeton,USA Alan J. Bishop Faculty of Education, Monash University, Melbourne, Australia Alexandre V. Borovik Department of Mathematics, The University of Manch- ester, Manchester, UK Rogério Monteiro de Siqueira School of Arts, Sciences and Humanities of the University of São Paulo, São Paulo, Brazil Silvia De Toffoli Philosophy Department, Stanford University, Stanford, CA, USA Paul Ernest School of Education, University of Exeter, Exeter, UK José Ferreirós Facultad de Filosofia, Universidad de Sevilla, Sevilla, Spain Slava Gerovitch Department of Mathematics, Massachusetts Institute of Tech- nology, Cambridge, MA, USA Valeria Giardino Laboratoire d’Histoire des Sciences et de Philosophie— Archives Henri-Poincaré, UMR 7117 CNRS—Université de Lorraine, Nancy, France Katalin Gosztonyi Bolyai Institute, University of Szeged, Szeged, Hungary; Laboratoire de Didactique André Revuz, University Paris Diderot - Paris 7, Paris, France Gila Hanna Department of Curriculum, Teaching, and Learning, University of Toronto, Toronto, Canada vii viii Contributors Matthew Inglis Mathematics Education Centre, Loughborough University, Leicestershire, UK Mikkel Willum Johansen Department of Science Education, University of Copenhagen, Copenhagen, Denmark Veselin Jungic Department of Mathematics, Simon Fraser University, Burnaby, Canada Stav Kaufman Cohn Institute, Tel Aviv University, Tel Aviv, Israel Brendan Larvor School of Humanities, University of Hertfordshire, Hatfield, Hertfordshire, UK Snezana Lawrence Institute for Education, Bath Spa University, Bath, UK Tony Mann Department of Mathematical Sciences, University of Greenwich, Greenwich, UK John Mason Department of Mathematics and Statistics, Open University, Milton Keynes, UK; University of Oxford, Oxford, UK Morten Misfeldt Department of Education, Learning and Philosophy, Aalborg University, Copenhagen, Denmark Madeline Muntersbjorn Department of Philosophy and Religious Studies, University of Toledo, Toledo, OH, USA Markus Pantsar Department of Philosophy, History, Culture and Art Studies, University of Helsinki, Helsinki, Finland Manya Raman-Sundström Department of Science and Mathematics Education, Umeå University, Umeå, Sweden Colin J. Rittberg School of Humanities, University of Hertfordshire, Hertford- shire, UK; Vrije Universiteit Brussel, Brussels, Belgium Emil Simeonov Department Applied Mathematics & Science, University of Applied Sciences Technikum Wien, Wien, Austria HenrikKraghSørensen DepartmentofMathematics,CentreforScienceStudies, Aarhus University, Aarhus, Denmark Editorial Introduction Brendan Larvor 1 Why Mathematical Cultures? Mathematicshasinternationallysharedstandardsofvalidity.Nevertheless,thereare local mathematical cultures, which can affect the direction and character of math- ematicalresearch.Therefore,philosophersofmathematicsandotherswhostudythe growthandepistemologyofmathematicsshouldhaveaninterestinthem.Theyalso matter because of the wider cultural importance of mathematics. Mathematics enjoys enormous intellectual prestige, and recent years have seen a growth of popular expository publishing, films about mathematicians, novels and plays. However, this same intellectual prestige encourages disengagement from mathe- matics. Ignorance of even rudimentary mathematics remains socially acceptable. Policy initiatives to encourage the study of mathematics usually emphasise the economic utility of mathematics. Appeals of this sort do not seem to be effective, perhaps because they speak to the needs of the nation rather than the interests of individual students, many of whom notice that it ispossible todo very wellin our economy without knowing very much mathematics. Moreover, policy responses rarely address an unhelpful perception of mathematics as remote and forbidding. There-presentationofmathematicsascultureoffersthepossibilityofanalternative approach, in which mathematics might enjoy the same appeal as the study of literatureor history.Thatis tosay, we might re-frame thestudy of mathematics as training oftheintellect, thefurnishingofawell-stocked mindandtheappreciation of local, national or global cultural riches. B.Larvor(&) SchoolofHumanities,UniversityofHertfordshire,HatfieldAL109AB,UK e-mail:[email protected] ©SpringerInternationalPublishingSwitzerland2016 1 B.Larvor(ed.),MathematicalCultures,TrendsintheHistoryofScience, DOI10.1007/978-3-319-28582-5_1
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