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50年国际数学奥林匹克50th IMO:50 Years of International Mathematical Olympiads(2011)

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50年国际数学奥林匹克50th IMO:50 Years of International Mathematical Olympiads(2011)

50thIMO–50YearsofInternationalMathematicalOlympiads−HansDietrichGronauHannsHeinrichLangmannDierkSchleicherEditors50thIMO–50YearsofInternationalMathematicalOlympiads123EditorsHansDietrichGronauUniversitätRostockInstitutfürMathematikUlmenstr.6918051RostockGermanygronauunirostock.deDierkSchleicherJacobsUniversityResearchICampusRing128759BremenGermanydierkjacobsuniversity.deHannsHeinrichLangmannBildungBegabunggemeinnützigeGmbHBundeswettbewerbMathematikKortrijkerStr.153177BonnGermanylangmannbundeswettbewerbmathematik.deISBN9783642145643eISBN9783642145650DOI10.1007/9783642145650SpringerHeidelbergDordrechtLondonNewYorkMathematicsSubjectClassification201000A09c©SpringerVerlagBerlinHeidelberg2011Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.CoverdesignWMXDesignGmbH,HeidelbergPrintedonacidfreepaperSpringerispartofSpringerScienceBusinessMediawww.springer.comPrefaceFrom10to22July2009Germanyhostedthe50thInternationalMathematicalOlympiadIMO.ThisjubileeanniversaryeventtookplaceonthecampusofJacobsUniversityBremen.Forthefirsttimethenumberofparticipatingcountriesexceeded100,with104countriesfromallcontinentssendingadelegationconsistingofsixstudents,aleaderandadeputyleader.Celebratingthe50thanniversaryoftheIMOprovidesanidealopportunitytolookbackoverthepastfivedecadesandtoreviewitsdevelopmentfrommodestbeginningstobecomeaworldwideevent.ThisbookisaimedatstudentsintheIMOagegroupandseekstodemonstratethatmathematicsisanactiveandlivelysubject,thousandsofyearsoldandyetyoungandfreshasever.WehaveinvitedseveralIMOpioneerstotellusaboutthedevelopmentofIMOsinceitfirstbegantheyrevealthatinitiallynobodythoughtitwoulddevelopintoanannualevent,letalonegrowasbigasitistoday.WeincludethreeaccountsfromIMOpioneersMirceaBecheanufromRomania,speakingonbehalfofthecountrythatcreatedtheIMOandhostedtheinitialOlympiadeventIstvánReimanfromHungarywhopersonallyexperiencedtheearlyyearsandWolfgangEngelfromthenEastGermanywhowitnessedtheimpacttheOlympiadshavehadfromtheoutsetonmathematicalactivitiesforstudents,particularlyinGermany.Thesereportsgiveavividandpersonaldescriptionofwhatgraduallybecameaninternationalsuccessstory.Alsoincludedisdataaboutthe50annualOlympiadswhichillustratesthedevelopmentofthecompetitionfromjustsevencountriesin1959to104countries,with565participants,in2009.Welistthemostsuccessfulcontestants,theresultsofthe50Olympiadsandthenamesofall112countriesthathaveevertakenpart.Inmathematics,talentisoftendevelopedanddemonstratedatanearlyage.ThusitisimpressivetoseethatmanyoftheworldsleadingresearchmathematicianswereamongthemostsuccessfulIMOparticipantsintheiryouth.ToillustratethisweincludealistshowingwinnersofprestigiousresearchawardswhoparticipatedintheIMOwhentheywereyoung.InadditiontothemathematicscompetitionanimportantaspectoftheOlympiadsisthatstudentsfromallovertheworldmeetandexchangeideas.ItisbothapersonalvviPrefacehighlightoftheirlivesthattheytreasureforalongtimeandaplacewhereinternationalfriendshipsdevelop.SomeofthepersonaloramusinganecdotesofpreviousIMOsareincludedinthelastchapterofthebook.Theoutstandingeventofthe2009OlympiadwasthecelebrationoftheIMOs50thanniversary.Sixoftheworldsleadingmathematicians,allofthemhighlysuccessfulformerIMOparticipants,wereinvitedasguestsofhonourtogivepresentationsBélaBollobás,TimothyGowers,LászlóLovász,StanislavSmirnov,TerenceTaoandJeanChristopheYoccoz.Theircontributionsarealsoincludedinthisbook.Wewouldliketoexpressoursinceregratitudetoallthosewhosupportedtheorganisationofthe50thIMO,makingitamemorableanduniqueeventforallparticipants.Finally,wewishtothanktheSpringerVerlagforpublishingthisbook.WeareindebtedtoClemensHeineforhissupportandcollaboration.Rostock,Bonn,BremenHansDietrichGronauMay2010HannsHeinrichLangmannDierkSchleicherWelcomeMessageDearIMOparticipants,ThisyearsIMOhasaspecialsignificancewecelebratethe50thanniversaryoftheIMO.InthebeginningsitstartedasaonetimeeventforstudentsfromthecountrieswhichatthetimeweresaidtoformthesocialistblockorSovietblock,towitBulgaria,Czechoslovakia,GermanDemocraticRepublic,Hungary,Poland,RomaniaandtheSovietUnion.Itisremarkablethatofthose7countries,3donotexistanymore.ButtheIMO,which,encouragedbythesuccessofthefirstcompetitionbecameayearlyevent,flourishes.Somekeydates1967thefirstWestEuropeancountriesUnitedKingdom,France,Italy,Swedentakepartinthe9thIMOinCetinje,Yugoslavia.Finlandsonetimeparticipationin1965hadnoimmediatecontinuation.TheNetherlandsfollowedsuitin1969,Austriain1970.TwononEuropeansocialistcountriesparticipatedinthe60sandearly70sMongoliasince1964andCubasince1971.The16thIMOin1974inErfurtEastGermanysawatruebreakthroughtheteamsoftheUSAandofVietnamparticipatedforthefirsttime.LienzAustriawasthevenueofthefirstWesternIMOin1976,Washington,DCofthefirstnonEuropeanIMOin1981.Australiaorganizedthe1988IMOinCanberra,thefirstAsianIMOtookplacein1990inBeijing,China.Argentinawasthevenueofthe1997IMOwearelookingforwardtoanIMOonAfricansoilinthenottoofarawayfuture.MysincerehopeisthatmoreandmorecountrieswilljointheIMOcommunityoldparticipatingcountrieswillseemoreandmorebenefitfromtheIMOfortheirownmathematicaleducationsystemandmathematicaltalentsearchandtheIMOwillcontinuetobeasuccessstoryinthenext50years.Bremen,July2009JózsefPelikánChairmanoftheIMOAdvisoryBoardviiviiiWelcomeMessageJózsefPelikánHungaryJózsefPelikántookpartin4IMOsinhisstudentdaysIn1963hewonasilvermedal,andin19646566threegoldmedals.Hewasalsoawardedtwicewithaspecialprizeforanoutstandingsolutionofaproblem.Since1971hehasbeenteachingatE˝otv˝osLorándUniversity,Budapest,Hungary.Heparticipatedintheorganizationofthe1970IMOheldinKeszthely,Hungary,andwasoneofthechieforganizersofthe1982IMOinBudapest,Hungary.HehasbeentheleaderoftheHungarianIMOteamsince1988.HewasanelectedmemberoftheIMOAdvisoryBoardbetween1992and2002,andhasbeentheChairmanoftheIMOAdvisoryBoardsince2002.

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