Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer: Volume 2: Hope and Disillusion PDF
Preview Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer: Volume 2: Hope and Disillusion
MYSTIC, GEOMETER, AND INTUITIONIST This page intentionally left blank M Y S T I C, G E O M E T E R, A N D I N T U I T I O N I S T The Life of L. E. J. Brouwer 1881–1966 Volume2 Hope and Disillusion DIRK VAN DALEN DepartmentofPhilosophy UtrechtUniversity CLARENDON PRESS • OXFORD 2005 3 GreatClarendonStreet,OxfordOX26DP OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwidein Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam OxfordisaregisteredtrademarkofOxfordUniversityPress intheUKandincertainothercountries PublishedintheUnitedStates byOxfordUniversityPressInc.,NewYork (cid:1)c DirkvanDalen,2005 Themoralrightsoftheauthorhavebeenasserted DatabaserightOxfordUniversityPress(maker) Firstpublished2005 Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, withoutthepriorpermissioninwritingofOxfordUniversityPress, orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate reprographicsrightsorganization.Enquiriesconcerningreproduction outsidethescopeoftheaboveshouldbesenttotheRightsDepartment, OxfordUniversityPress,attheaddressabove Youmustnotcirculatethisbookinanyotherbindingorcover andyoumustimposethissameconditiononanyacquirer BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressCataloguinginPublicationData Dataavailable ISBN0–19–851620–7 978-0-19-851620-0 TypesetbySPIPublishersServices,Pondicherry,India PrintedinGreatBritainonacid-freepaperbyBiddlesLtd.,King’sLynn,Norfock 10 9 8 7 6 5 4 3 2 1 DEDICATION Dedicated to the Mathematical Research Institute at Oberwolfach– the organiza- tion and all members of staff– in appreciation of its major role in re-establishing mathematicsinafreeEurope,itsroleinpromotinginternationalco-operation,and foritsgenerosityandencouragement,fromwhichthepresentbookalsobenefited This page intentionally left blank PREFACE Faire abstraction du monde d’objects (ce quiestne´cessairepourtravailler dansles mathe´matiquesintuitionistes)n’estpossi- blequ’ene´prouvantlaviecommeunreˆve. Brouwer. InthetwentiesBrouwerhadreachedtheundisputedstatusofmastertopologist andmysteriousrevolutionary.Hehadgiventopologyanewleaseoflife;hisinno- vationsandhisalmostmagicalintuitiondeterminedtoalargeextentthecourseof topologicalresearchinthefirsthalfofthecentury.Ithadsurprisedtheprofessional worldthatthisgeniushadturnedhisbackontraditionalmathematicsandstarteda thoroughrevisionofthefoundationsofhissubject.Involume1wehavesketched thebasicideasandprinciplesofhisintuitionism;inthisvolumewewillconcentrate largelyonthereception(andrejection)ofhisprogramme.Lookingdispassionately attheturbulentyearsthatfollowedafter1920,wecanbutconcludethatBrouwer did not seek the conflict. His papers were technical and almost dull; if there was anyprovocationatall,itwasinthesubjectmatter,notinsurreptitiousattacks. It has been Brouwer’s misfortune that his name usually came up in conjuction withHilbert’s.Initselfthatwasnothingtobeashamedof;afterall,DavidHilbert wasthemanwhosucceededPoincare´ astheunchallengedmasterofmathematics. Unfortunately a comparison between Brouwer and Hilbert was not particularly instructive or clarifying. It is difficult to find two mathematical geniuses of such totallyoppositecharacter.TheDutchmanwastheartistic,unfetteredscientist,with an unbridled lust for travelling and friendships, while at the same time practicing meditation and entertaining austere moral and political convictions. A man who felt at home in salons as well as in the company of esoteric revivalists, who could be totally absorbed in mathematics, but who could equally well leave the subject alone;whohadareputationfordefendinglostcauses,andwhorefusedtosacrifice themoralissuetopersonalcomfort. ThegreatGo¨ttingerwasastrongsingle-mindedspecialist,whodevotedhislife tothecultivationofmathematicsandphysics.Amanwhosemindneverleftmathe- maticsalone,whonimblyjumpedfromoneareatoanothertoperformmiracles.A manwithjusttwogoalsinlife:mathematicsandGo¨ttingen,goalsthatwerelargely attainedbyhissheermathematicalintellectandhistalentforleadership.Thefol- lowingchapterswillshowthataconflictbetweenthetwowasnotapredetermined matter. One may well conjecture that without the First World War, there would not have been a conflict. As the reader will see, the Grundlagenstreit greatly exas- perated Hilbert, and the exchange of the twenties was not always kept within the confinesofscholarlycourtesy,butwithoutthepoliticalcomplicationstherewould not have been the fateful act that brought Einstein to the exclamation ‘I would neverhavethoughtthatHilbertwascapableofsuchemotionaloutbursts.’ viii PREFACE Both men would have coexisted peacefully with now and then a scientific exchange on foundational matters. Hilbert’s Programme would have been killed byGo¨del,sotospeak,beforeaseriousconflictcouldhaveerupted. The documents used in the present volume come mostly from sources men- tionedinvolume1.Thereis,however,acertainamountofnewmaterialfromvar- iousarchives,tomentionthemajorsources:thearchivesofBieberbach,Courant, Doetsch,Hilbert,HkdeVries,St.John’sCollegeCambridge,HeidelbergUniver- sity,NationaalArchiefDenHaag. Since the publication of the first volume a number of relevant historical studies have appeared; the following old and new texts have been useful in pro- viding information on various topics: [Blauwendraat 2004], [Georgiadou 2004], [Groot 1946], [Hesseling 2003], [Hu¨bner 2002], [Johnson 1979,Johnson 1981], [Knegtmans 1998], [Maas 2001], [Menger 1979,Menger 1994], [Urysohn1951], [Schroeder-Gudehus1966],[Segal1986],[Siegmund-Schultze2001]. The references in this volume to Brouwer’s publications do not match the list ofvolume1. ThecorrespondenceofBrouwerwillinduetimebepublished,theworkiscar- riedoutaspartoftheBrouwerprojectinUtrecht.AsimilarprojectforBrouwer’s unpublishedmanuscriptsisenvisaged. To the long list of those who supported me with information and advice, I amhappytoaddthenamesofS.M.P.Brouwer-Euwe,FelixBrowder,T.Corkery, JonathanHarrison,HansHuebner,C.B.J.Jonkers,HansEwaldKeszler,R.vander Laan-van Heemert, M.S.van Leeuwen-Boomkamp, Eckart Menzler-Trott, Agnes vanNoort,VolkerRemmert,BertSchweizer,PaulvanUlsen. IhardlyneedrepeatwhatIsaidaboutthecooperationwithmywifeinvolume I,shewasagainineveryrespectmypartnerinthisjointproject. OvertheyearsmyindebtednesstotheMathematicalInstituteatOberwolfach has been accumulating. I started by attending the annual meetings on geometry, these were followed by meetings on logic, but gradually the institute became a friendlyretreatwhereIcouldconcentrateonthebiographyofBrouwer,awayfrom thedistractioncalleduniversity.Likemanybeforeandafterme,Icametoappre- ciatetheinstituteastheidealplaceforexchangeofideas,research,andreflection. IammostgratefultotheOberwolfachestablishmentandtheeversupportivestaff members, who managed to turn the institute into a mathematician’s home away fromhome. Utrecht,June2005 CONTENTS 12 TheFathersofDimension 441 12.1 ThetwoRussians 441 12.2 Thedefinitionofdimension 444 12.3 TheVienneseconnection 467 12.4 ThescientificlegacyofUrysohn 470 13 Progress,recognition,andfrictions 481 13.1 Thefirstskirmishesinthefoundationalconflict 481 13.2 Consolidationandentrenchment 493 13.3 TheRiemannvolume 503 13.4 Internationalrelations 508 13.5 TheDutchtopologicalschool 514 14 FromBerlintoVienna 538 14.1 Moreintuitionism 538 14.2 FeelingsofcrisisandGermanscience 540 14.3 TheBerlinlectures 544 14.4 TheViennalectures 561 14.5 Otheractivities 569 15 ThethreeBattles 573 15.1 TheGrundlagenstreit 573 15.2 TheBolognaconference 587 15.3 Thewarofthefrogsandthemice 599 15.4 TheendingsoftheGrundlagenstreit 636 15.5 TheMengerconflict 643 16 TheThirties 672 16.1 Freudenthalarrives 673 16.2 Intuitionisticlogic 676 16.3 TheSodalitasaffair 678 16.4 Go¨ttingen’sfateundertheNazi’s 693 16.5 Bieberbach’sconversion 695 16.6 CompositioMathematica 703 16.7 Go¨ttingenreconsidered? 710 16.8 Dutchaffairs 715 17 WarandOccupation 738 17.1 OccupiedHolland 738 17.2 Weitzenbo¨ck’schoice 740
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