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1、theotherway.Youshouldnotregardmathematicsasaclosedworld,andtheinteractionbetweenmathe-AdvicetoaYoungMathematicianmaticsandotherdisciplinesishealthybothfortheindividualandforsociety.MichaelAtiyahPsychologyBecauseoftheintensementalconcentrationrequiredWarninginmathematics,psychologicalpressu
2、rescanbeconsid-Whatfollowsisverymuchapersonalviewbasedonerable,evenwhenthingsaregoingwell.Dependingonmyownexperienceandreflectingmypersonality,theyourpersonalitythismaybeamajororonlyaminortypeofmathematicsthatIworkon,andmystyleproblem,butonecantakestepstoreducetheten-ofwork.However,mathemat
3、iciansvarywidelyinallsion.Interactionwithfellowstudents—attendinglec-thesecharacteristicsandyoushouldfollowyourowntures,seminars,andconferences—bothwidensone’sinstinct.Youmaylearnfromothersbutinterpretwhathorizonsandprovidesimportantsocialsupport.Tooyoulearninyourownway.Originalitycomesbyb
4、reak-muchisolationandintrospectioncanbedangerousingaway,insomerespects,fromthepracticeoftheandtimespentinapparentlyidleconversationisnotpast.reallywasted.Collaboration,initiallywithfellowstudentsorone’sMotivationsupervisor,hasmanybenefitsandlong-termcollabo-rationwithcoworkerscanbeextremely
5、fruitfulbothinAresearchmathematician,likeacreativeartist,hasmathematicaltermsandatthepersonallevel.Thereistobepassionatelyinterestedinthesubjectandfullyalwaystheneedforhardquietthoughtonone’sown,dedicatedtoit.Withoutstronginternalmotivationbutthiscanbeenhancedandbalancedbydiscussionyoucann
6、otsucceed,butifyouenjoymathematicstheandexchangeofideaswithfriends.satisfactionyoucangetfromsolvinghardproblemsisimmense.ProblemsversusTheoryThefirstyearortwoofresearchisthemostdifficult.Thereissomuchtolearn.Onestrugglesunsuccess-Mathematiciansaresometimescategorizedaseitherfullywithsmallprob
7、lemsandonehasseriousdoubts“problemsolvers”or“theorists.”Itiscertainlytrueaboutone’sabilitytoproveanythinginteresting.Ithatthereareextremecasesthathighlightthisdivi-wentthroughsuchaperiodinmysecondyearofsion(Erd˝osversusGrothendieck,forexample)butresearch,andJe
