Against All Odds: Women’s Ways to Mathematical Research Since 1800 PDF
Preview Against All Odds: Women’s Ways to Mathematical Research Since 1800
Women in the History of Philosophy and Sciences 6 Eva Kaufholz-Soldat Nicola M. R. Oswald Editors Against All Odds Women’s Ways to Mathematical Research Since 1800 Women in the History of Philosophy and Sciences Volume 6 Series Editors Ruth Edith Hagengruber, Department of Humanities, Center for the History of Women Philosophers, Paderborn University, Paderborn, Germany MaryEllenWaithe,ProfessorEmerita,DepartmentofPhilosophyandComparative Religion, Cleveland State University, Cleveland, OH, USA GianniPaganini,DepartmentofHumanities,UniversityofPiedmont,Vercelli,Italy As the historical records prove, women have long been creating original contributions to philosophy. We have valuable writings from female philosophers from Antiquity and the Middle Ages, and a continuous tradition from the Renaissancetotoday.Thehistoryofwomenphilosophersthusstretchesbackasfar as the history of philosophy itself. The presence as well as the absence of women philosophersthroughoutthecourseofhistoryparallelsthehistoryofphilosophyas a whole. Edith Stein, Hannah Arendt and Simone de Beauvoir, the most famous representatives of this tradition in the twentieth century, did not appear form nowhere. They stand, so to speak, on the shoulders of the female titans who came before them. The series Women Philosophers and Scientists published by Springer will be of interestnotonlytotheinternationalphilosophycommunity,butalsoforscholarsin history of science and mathematics, the history of ideas, and in women’s studies. More information about this series at http://www.springer.com/series/15896 Eva Kaufholz-Soldat Nicola M. R. Oswald (cid:129) Editors Against All Odds ’ Women s Ways to Mathematical Research Since 1800 123 Editors EvaKaufholz-Soldat NicolaM. R.Oswald Goethe University Frankfurt DepartmentofMathematicsandInformatics Frankfurtam Mainu, Hessen,Germany University of Wuppertal Wuppertal, Nordrhein-Westfalen, Germany ISSN 2523-8760 ISSN 2523-8779 (electronic) Womenin the History of Philosophy andSciences ISBN978-3-030-47609-0 ISBN978-3-030-47610-6 (eBook) https://doi.org/10.1007/978-3-030-47610-6 ©SpringerNatureSwitzerlandAG2020 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 authors or the editors give a warranty, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Series Foreword Women in the History of Philosophy and Sciences Thehistoryofwomen’scontributionstophilosophyandthesciencesdatesbackto the very beginnings of these disciplines. Theano, Hypatia, Du Châtelet, Agnesi, Germain, Lovelace, Stebbing, Curie, Stein are only a small selection of prominent women philosophers and scientists throughout history. TheSpringerSeriesWomenintheHistoryofPhilosophyandSciencesprovidesa platform for publishing cutting-edge scholarship on women’s contributions to the sciences,tophilosophy,andtointerdisciplinaryacademicareas.Wethereforeinclude inour scope women’scontributions tobiology, physics,chemistry and related sci- ences.TheSeriesalsoencompassestheentiredisciplineofthehistoryofphilosophy since antiquity(includingmetaphysics,aesthetics, philosophy ofreligion. Wewel- comealsoworkaboutwomen’scontributionstomathematicsandtointerdisciplinary areassuchasphilosophyofbiology,philosophyofmedicine,sociology. Theresearchpresentedinthisseriesservestorecoverwomen’scontributionsand to revise our knowledge of the development of philosophical and scientific disci- plines, so as to present the full scope of their theoretical and methodological tra- ditions. Supported by an advisory board of internationally esteemed scholars, the volumes offer a comprehensive, up-to-date source of reference for this field ofgrowing relevance. See the listing of planned volumes. The Springer Series Women in the History of Philosophy and Sciences will publish monographs, handbooks, collections, anthologies, and dissertations. Paderborn, Germany Ruth Hagengruber Cleveland, USA Mary Ellen Waithe Vercelli, Italy Gianni Paganini v Introduction Virginia Woolf once famously claimed that “a woman must have money and a roomofherownifsheistowritefiction”(Woolf[1929],p.4).Sincemostwomen depended economicallyonamalefigure, whetherahusband orfather,they lacked suchmeans;this,inWoolf’seyes,providedanexplanationforthesmallnumberof female authors up until her day. Clearly, just as was the case with careers in literature, so with mathematics; there were only a few female mathematicians beforethemiddleofthetwentiethcentury.Eventoday,farfewerwomenthanmen hold professorships in mathematics. Thus, this volume raises an analogous ques- tion: What did it take for a woman to become a mathematician? Woolflookedathistoricalexamplesandsodotheessaysinthisvolume,which describe the lives of a variety of mathematicians from the eighteenth through the twentiethcenturies.ButwhereasWoolfcametoherconclusionbylookingatthings women lacked, this book takes a different approach—by analyzing some of those women who actually did manage to receive academic training and go on to do creativeworkinmathematics.Sincethesewomenwereabletofindtheirwayintoa very patriarchal and hegemonic world, by looking at these cases certain possibili- ties,howeverlimited,becomeevident.Thepluralalreadyhintsatavitaldifference when compared with Woolf’s seemingly universal solution: there was and never will be a single way for women to become mathematicians, even if one can find plenty of common circumstances. As will become clear, each of the women por- trayed here eventually found individual solutions that depended heavily on the specific situation in different countries during the period in question. Though we have grouped the essays in this volume into four thematic sections—three with introductoryreflectionsbyNicolaOswald—Iwillherediscussthesecasesroughly in chronological order. My aim is to provide some historical background that will highlight and contextualize important milestones in the timeline of women’s edu- cation, especially in the field of mathematics. Let me remark to begin with that we, too, cannot ignore what was lacking. We need to familiarize ourselves with the obstacles in order to understand how some women were able to overcome them. Without higher education—or barely any education at all for most girls until well into the nineteenth century and in many vii viii Introduction countries long after that—mathematics could only be studied in private. Such women invariably came from progressive and, more often than not, wealthy fam- ilies. Only in these special circumstances did young women have access to books andthetimetoreadthem.Itiscertainlynocoincidencethatmanyofthefirstfemale mathematicians—Celia Grillo Borromeo(1684–1777),1Émilie duChâtelet(1706– 1749), Maria Gaetana Agnesi (1718–1799), Ada Lovelace (1815–1852)—came fromanoblebackground.ThesameholdsforSophieGermain(1776–1831),whose careerwewilldiscussshortly.First,however,letussetthestagebytakingacloser look at the period she lived in by considering certain aspects that reflect the rela- tionship between science and gender at that time. According to Londa Schiebinger, theeighteenth century was characterized by a rather rapid and finally peremptory exclusion of women from science, which from then on was predominantly practiced at academies and universities, which were exclusively reserved for men (Schiebinger [1989]). Criticism of this thesis was brought forward by scholars such as Lorraine Daston, who pointed out that Schiebinger was mainly talking about singularities when she pointed to artisan families and aristocratic salons as examples of a much friendlier attitude towards women in science during the Enlightenment (Daston [1989], p. 1502). Subsequent publications,however,suchas(Mommerts[2002]),showthatatleastsomewomen carried out scientific endeavors during this period, albeit well hidden from the public eye; they stayed behind the scenes, while the men took center stage. If we take into account the female mathematicians cited above, I believe the topic of exclusion of women from science during the eighteenth century stands in need of reassessment. Another line of argument in Schiebinger’s book, however, is indisputable. Aristotle (384–322 BC) argued that women were essentially inferior to men, in particular with respect to their bodies and their reproductive organs. This view became entrenched through Galen (129 AD–c. 200/c. 216), who shaped medical discourse for centuries to come. Schiebinger shows how this claim influenced the drawings offemale skeletons, which appeared as mild modifications of male ones (Schiebinger[1989],chapter7).Suchdrawingsrevealedfewsignificantdifferences beforethetwosexeswereinvented/discoveredandunderstoodasincommensurable in the eighteenth century (Laqueur [1992], pp. 151–152). Another assumption made by Aristotle survived even longer. Understanding women to be inferior or incomplete males, the philosopher claimed they had characteristics complementary to those of men. Over time, those characteristics were linked more and more to what were considered the natural destinies of each sex:womenwererelegatedtotheprivatesphereofthehomeaswivesandmothers; men were destined to be actors in the public sphere (Hausen [1976]). Within this tradition,onesawwomenasendowedwithimaginationandcreativity,facultiesthat 1SinceBorromeoisratherunknown,letusjustnoteinpassingthathermostimportantresultwas arguablythediscoveryoftheClélie,asin“thecurveofCelia”.Thissphericalcurveisgivenbythe propertythattheangleoflongitudeisamultipleoftheangleofcolatitude.Thus,asphericalspiral, e.g.isaspecialcaseoftheClélie. Introduction ix were long associated with cunning and deception. During the eighteenth century, however, in the wake of a growing veneration for literati and the cult of (male) genius,theseformerlyfemalecharacteristicssuddenlybecamedesirable.Yetrather than now being ascribed to both sexes, they were simply declared male attributes (Daston [2008]). Imagination and creativity, being abilities demanded of poets, artists, and writers, were apparently talents that women simply lacked. This sweeping argument or prejudice was enough to discourage most women from pursuingtheseavocations,atopicWoolftoucheduponinheressay(Woolf[1929], pp.39–41).Yet,infact,manyofhercontemporariessawaclearconnectionwithall forms of intellectual endeavor, including mathematics. For them, the female intellectwasmerelycapableofimitatingand,asinchildbirth,reproducing.Hence, following this traditional view, most believed that while women could perform calculations following careful instructions, men alone could do original mathe- matical work, proving theorems and creating interesting hypotheses (Kaufholz-Soldat [2017], pp. 204–205). This overall background has clear relevance for the second part of Jenny Boucard’s essay on Sophie Germain. Born in 1776, Germain was excluded from academiccirclesandthuscouldonlystudymathematicsinprivate.Herpredicament led her to take on a false identity, and she presented herself in letters to Carl Friedrich Gauß (1777–1855) as Monsieur Antoine-Auguste Le Blanc. After pre- sentingGermain’sbiographyandanoverviewofhermathematicalworks,Boucard takesacloserlookatthereceptionoftheFrenchmathematicianattheturnfromthe nineteenth to the twentieth century. This shows that Germain was not only pre- sented as an inspirational role model for young girls. Indeed, critical voices were alsoraised,questioninghermathematicalabilitiesandthoseofwomeningeneral,a tropethatcanalsobefoundinthereceptionofSofjaKovalevskaya(1850–1891)in the years after her sudden death (Kaufholz-Soldat [2019]). This view shifted later, as Boucard shows, when Germain’s mathematical works came to be appreciated more and more, especially after her correspondence with Gauß was rediscovered beginning at the end of the 1870s. The Belgian mathematician Paul Mansion (1844–1919) called her a “competent reader” of Gauß’s writings. Still, even this positive assessment was nonetheless consistent with the view of those who, while concedingwomenthepossibilitytocomprehendatleastsomepartsofmathematics, deniedtheirabilitytodocreativework(cf.e.g.Loria[1903;1904],Möbius[1905], Münsterberg [1897], p. 349). The other women portrayed in this volume were born quite a bit later, and thus experienced very different circumstances once institutions of higher education gradually began to open their doors to women. Throughout continental Europe— whetherinFrance(Christen-Lécuyer[2000]),Germany,orSwitzerland—foreigners weremoreoftenthannotthefirstwalkthroughthosedoors.Thisreflectedadouble standard that was particularly striking in the Swiss case, since already in 1867 the universities allowed international students to matriculate regardless of their sex. Swiss women, on the other hand, could not even attend a Gymnasium to gain the Abitur, which was required for Swiss citizens who wanted to study at a university (Creese & Creese [2004], p. 181). x Introduction Asimilarsituationprevailed intheGerman states duringthenineteenthcentury up until 1893 when Karlsruhe in the state of Baden allowed women to attend a Gymnasium for the first time.2 Thus, it comes as no surprise that the first female students at German universities came from abroad as well. Most came from English-speaking countries after having studied beforehand at elite women’s col- leges.TheoldestofthesewasGirtonCollege,Cambridge, foundedin1869;inthe UnitedStatesofAmerica,VassarCollegewasthefirsttoopenin1865,followedby Smith and Wellesley in 1871 and 1875, respectively (Parshall [2015], p. 72f.). However,BrynMawr,whichopenedin1885,wastheonlywomen’scollegeinthe United States to grant Ph.D.’s (Green & LaDuke [1987], p. 12). For this very reason, and the excellent reputation German mathematics enjoyed at the time, two Americans—Mary Frances Winston (1869–1959) and Magaret Maltby (1844–1960)—as well as Grace Chisholm (1868–1944) from England enrolled in the mid-1890s at the Prussian University of Göttingen. Not until 1908 would German women be allowed to matriculate at Prussian universities. It was partlyduetoFelixKlein’s(1849–1925)influentialcontactsinthePrussianMinistry of Culture that these foreign women gained permission to enroll as part of an experiment to ascertain women’s ability to undertake university studies. In her essay, Renate Tobies’ takes a closer look at how Klein and his colleague David Hilbert(1862–1943)madetheiruniversityintoahubforthisgenerationofwomen in mathematics, thereby serving as a forerunner for Prussia as well as the other German states. Drawing on archival sources, Tobies gives an extensive overview of the women attending Klein’s and Hilbert’s seminars between 1893 and 1912. This study thus further elaborates on the findings in (Tobies [1991/92, 1997, 1999]), which confirm and consolidate Göttingen’s reputation as a female-friendly university for mathematics and other related fields. Tobies’ essay offers an important supplement to the relatively large body of workonGöttingen,whereastheotheressaysinthischapterlookatuniversitiesthat have not received much attention from historians, insofar as female students of mathematics are concerned. Katharina Spiess examines the situation in Bavaria, comparingitsuniversityinWürzburgwithitscounterpartsinErlangenandMunich. WhilewomenwereonlyallowedtostudyatBavarianuniversitiesin1903,already in 1886 the American Marcella O’Grady (1863–1950) was allowed to attend biology courses at Würzburg. Still, it was not until 1912 that Bavarian women began to enroll in mathematics in Würzburg. Spiess carefully highlights the most importantfactorsforthisdelay,pointingclearlytotheroleoftheBavarianMinistry of Culture. Martina Bečvářová, on the other hand, considers the first women to earn their Ph.D.’s at the universities in Prague between 1900 and 1945. In a prosopographic study largely based on archival sourcesandinterviews, shewas able todetailtheir biographical background, more often than not for the first time. Moreover, the comparative overview of the situation at each university, in particular the careful distinctionbetweenGermanstudentsandthoseofCzechnationality,willhopefully 2BadenwasalsothefirstGermanstateallowingwomentostudyin1900.
The list of books you might like
