Research in History and Philosophy of Mathematics: The CSHPM 2015 Annual Meeting in Washington, D. C. PDF
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Proceedings of the Canadian Society for History and Philosophy of Mathematics La Société Canadienne d’Histoire et de Philosophie des Mathématiques Maria Zack Elaine Landry Editors Research in History and Philosophy of Mathematics The CSHPM 2015 Annual Meeting in Washington, D. C. Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques SeriesEditors MariaZack ElaineLandry Moreinformationaboutthisseriesathttp://www.springer.com/series/13877 Maria Zack • Elaine Landry Editors Research in History and Philosophy of Mathematics The CSHPM 2015 Annual Meeting in Washington, D.C. Editors MariaZack ElaineLandry MathematicalInformation DepartmentofPhilosophy andComputerSciences UniversityofCalifornia,Davis PointLomaNazareneUniversity Davis,CA,USA SanDiego,CA,USA ISSN2366-3308 ISSN2366-3316 (electronic) ProceedingsoftheCanadianSocietyforHistoryandPhilosophyofMathematics/LaSociété Canadienned’HistoireetdePhilosophiedesMathématiques ISBN978-3-319-43269-4 ISBN978-3-319-46615-6 (eBook) DOI10.1007/978-3-319-46615-6 LibraryofCongressControlNumber:2016957647 MathematicsSubjectClassification(2010):01-06,01A72,01A99 ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisbookispublishedunderthetradenameBirkhäuser,www.birkhauser-science.com TheregisteredcompanyisSpringerInternationalPublishingAG,CH Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Introduction This volume contains seventeen papers that were presented at the 2015 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics (CSHPM). This was a special year, because the meeting was part of the Mathe- maticalAssociationofAmerica’sMathFestandwasajointmeetingoftheCSHPM with the British Society for the History of Mathematics (BSHM), the History of Mathematics Special Interest Group of the Mathematical Association of America (HOMSIGMAA),andthePhilosophyofMathematicsSpecialInterestGroupofthe MathematicalAssociationofAmerica(POMSIGMAA).Themeetingtookplacein Augustof2015inWashington,D.C. At this meeting the memories of Jacqueline (Jackie) Stedall and Ivor Grattan- Guinnesswerehonored,thecentennialoftheMathematicalAssociationofAmerica wascelebrated,andaspecialsessionontheimportanceofmathematicalcommuni- tieswasheld.Severalpapersinthisvolumeconnectwiththesethemes.Thepapers are arranged in roughly chronological order and contain an interesting variety of modernscholarshipinboththehistoryandphilosophyofmathematics. In “The Latin translation of Eucid’s Elements attributed to Adelard of Bath: relation to the Arabic transmission of al-Hajjaj,” Gregg De Young discusses new : evidence that supports the conclusion that the earliest Latin version of Euclid’s Elements,whichisderivedfromtheArabic,isbasedontheArabicversionattributed toal-Hajjaj. : ChristopherBaltus’s“Thearcrampantin1673:AbrahamBosse,FrançoisBlon- del,PhilippedelaHire,andconicsections”exposesthereaderto thearcrampant which is an arc of a conic section determined by tangents at two given endpoints andbyanadditionaltangentline.Intheseventeenthcentury,bothFrançoisBlondel and Philippe de la Hire independently worked on this interesting curve. In “The need for a revision of the prehistory of arithmetic and its relevance to school mathematics,”PatriciaBaggettandAndrzejEhrenfeuchtcontinuetheconversation about seventeenth-century mathematics by looking at the computational work of John Napier (1617) and the subsequent work of John Leslie (1817). They also v vi Introduction discuss how these ideas can be used to enrich student learning in twenty-first- centurymathematicsclassrooms. A significant number of the papers in this volume focus on nineteenth-century mathematics. In “Bolzano’s measurable numbers: are they real?” Steve Russ and Kateˇrina Trlifajová examine work done by Bolzano in the 1830s in Prague. At that time, Bolzano wrote a manuscript giving a foundationalaccount of numbers and their properties. This work was evidently an attempt to provide an improved proofofthesufficiencyofthecriterionusuallyknownasthe“Cauchycriterion”for theconvergenceofan infinitesequence.RogerGodardalso considersthe workof Bolzanoandseveralothersin“Findingtherootsofanonlinearequation:historyand reliability.”Inthispaper,Godardlooksatpartofthehistoryofnumericalmethods forfindingrootsofnonlinearequations. In addition to being the MAA Centennial, the year 2015 was also the 200th anniversaryofthebirthofGeorgeBoole,andthe150thanniversaryofthefounding of the London Mathematical Society, whose first president was Augustus De Morgan.Gavin Hitchcock has created a delightfulplay “Remarkable Similarities: A Dialogue Between Boole and De Morgan” which illuminates the relationship betweenthesetwomen,andthetextoftheplayispublishedinthisvolume.Francine Abeles looks at another important nineteenth-century friendship, the relationship between Charles Peirce and William Kingdon Clifford in “Clifford and Sylvester on the development of Peirce’s matrix formulation of the algebra of relations, 1870–1882.”Abeles is particularlyinterested in Pierce’s work to show that every associativealgebracanberepresentedbyamatrix. The British mathematician William Burnside, who was in the late nineteenth century a pioneer of group theory, spent most of his career at the Royal Naval College, Greenwich. Many believe that Burnside worked in isolation. Howeverin “The correspondenceof William Burnside,” Howard Emmens looks at some new evidence that may change that understanding of Burnside and his work. Another unexpectedpieceofscientifichistorycanbefoundinMichiyoNakane’s“Historical evidenceoftheclosefriendshipbetweenYoshikatsuSugiuraandPaulDirac.”Inthis paper,NakanelooksattherelationshipbetweenPaulDirac,J.RobertOppenheimer, andtheJapanesephysicistYoshikatsuSugiura.Theirfriendshipbeganinthe1920s whileSugiurawasstudyinginEurope,continuedafterSigiurahadreturnedtoJapan, and,surprisingly,enduredwellbeyondWorldWarII. For nearly 50 years, Ivor Grattan-Guinness was a significant force in the twentieth- and twenty-first-century history. Grattan-Guinness, who was an extremely prolific writer and collaborator, passed away in December of 2014. In “Grattan-Guinness’s work on classical mechanics,” Roger Cooke provides a carefullydocumentedsurveyof one partof Grattan-Guinness’significantbodyof scholarlywork. Mathematicsisahumanendeavorandhumanisticmathematicsemphasizesthat fact.In“Humanisticreflectionsonhundredthpowers:acasestudy,”JoelHaackand TimothyHallusetheirownexperienceinsolvingaproblemthatrecentlyappeared inMathematicsMagazinetoillustratethatsolutionsandproofscanbeapproached in a variety of ways and that it is possible for different strategies to offer unique insightsintotheproblem. Introduction vii SteveDiDomenicoandLindaNewmanarebothlibrariansandtackleanimpor- tant twenty-first-century issue in their paper “The quest for digital preservation: will a portion of mathematics history be lost forever?” This paper offers some importantcautionsfor all of us whose research is dependenton archivalmaterial. Libraries,archives,andmuseumshavetraditionallypreservedandprovidedaccess to many different kinds of physical materials, including books, papers, theses, facultyresearchnotes,correspondence,etc.However,inthemodernmathematical communitymuchoftheequivalentmaterialonlyexistselectronicallyonwebsites, laptops,privateservers,andsocialmedia.Ifthismaterialisgoingtobeofanyuseto futuregenerationsofresearchers,itmustbepreserved.Inthisarticle,DiDomenico andNewmandiscussseveralkeyissuesindigitalpreservation. In honor of the centennial of the Mathematical Association of America, sev- eral papers in this volume focus on mathematical communities, particularly the development of an American mathematical community in the twentieth century. In the first paper, “Mathematical communities as a topic and a method,” Amy Ackerberg-Hastingsdevelopsaformalhistoricaldefinitionfortheterm“mathemat- icalcommunities.”In“TheAmericanMathematicalMonthly(1894–1919):a new journal in the service of mathematics and its educators,” Karen Hunger Parshall looksatthefirsttwenty-fiveyearsofthepublicationoftheMonthlyinthecontextof theevolvingAmericanmathematicalcommunity.TheMonthlybecametheofficial publication of the Mathematical Association of America when it was founded in 1915. TheSmithsonian’sNationalMuseumofAmericanHistoryishometoanumber of interesting physical objects associated with the history of mathematics. In “ChartermembersoftheMAAandthematerialcultureofAmericanmathematics,” Peggy Aldrich Kidwell discusses several artifacts in the Smithsonian that are connected with charter members of the MAA. These objects are associated with avarietyofmathematicalactivitiesincludingresearchonprimenumbers,creating geometricmodelsforthe classroom,andencouragingparticipationin recreational mathematics. One of the significant changes in the United States in the twentieth century wasthe emergenceofan Americanmathematicalresearchcommunity.Likemany American mathematicians of his generation, Edward V. Huntington (1874–1952) began his mathematical studies in the United States, but completed his doctoral work in Germany. In “An American postulate theorist: Edward V. Huntington,” Janet Heine Barnett discusses one area of Huntington’s mathematical research and its connection to the development of the research agenda of the American postulate theorists. Well-prepared high school students are a critical component in maintaining a mathematical research community in the United States. The easternEuropeantraditionofusingMathCirclestopreparemathematicallytalented secondaryschoolstudentsformathematicalcompetitionsspreadtotheUnitedStates in the 1990s. In “The establishment and growth of the American Math Circle movement,”BrandyWiegersandDiana WhitelookatthegrowthofMathCircles andtheuniquewaysthattheyarebeingimplementedintheUnitedStates. viii Introduction Thiscollectionofpaperscontainsseveralgemsfromthehistoryandphilosophy of mathematics which will be enjoyed by a wide mathematical audience. This collection was a pleasure to assemble and contains something of interest for everyone. SanDiego,CA,USA MariaZack Davis,CA,USA ElaineLandry Editorial Board The editors wish to thank the following people who served on the editorial board forthisvolume: AmyAckerberg-Hastings UniversityofMarylandUniversityCollege ThomasArchibald SimonFraserUniversity JanetHeineBarnett ColoradoStateUniversity–Pueblo JuneBarrow-Green TheOpenUniversity DavidBellhouse UniversityofWesternOntario MariyaBoyko UniversityofToronto DanielCurtin NorthernKentuckyUniversity DavidDeVidi UniversityofWaterloo ThomasDrucker UniversityofWisconsin-Whitewater ix
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