第12期XXXX4下半月号本期四版notamathe

MartinGroetschel122010.4 1WewerehonoredtohaveaninformalmeetingwithSteveSmale,oneoftheFieldsMedalistswhoalsowontheprestigiousWolfPrize,onApril16th,2010,inPekingUniversity.Herewepresentthenoteofthetalk.Prof.LanWen:Wewillstartourinformalmeeting.HereisSteveSmale.SteveSmalehaslegendarylife,aseverybodyknows.Youcanaskwhateveryouwanttoknowabouthim,hisideas,orhowtodomathematics.Orhewillaskyouwhatyouwanttoknow.Prof.Smale:OK,whatdoyouwanttoknow?YanZou,seniorstudent:ThePoincaréconjectureindimensionthreewasnotproveninbytopology,butbygeometry.Whatdoyouthinkaboutit?Prof.Smale:Itisaproofbygeometry,asyousay.Idonʼtknowwhetheritisaninterestingquestionornottolookforanotherproofwhichismoretopological.Idonotknow.GrigoriPerelmanhasgotagoodproof.Itisanewmethodanditisfinetousedifferentialgeometryinp.d.e..YanZou,seniorstudnet:WhatdoyouthinkifitisapossiblewaytoprovePoincaréconjectureindimensionfour?Prof.Smale:Ithoughtaboutfiveormore.Ithoughtaboutthreesometimes,butIdidnotreallythinkaboutfourverymuch.Ijusthavelimitedresources.Therearevariousthingsintheworldformetothinkabout.ItʼsnotgoodformetothinkaboutPoincaréconjectureindimensionfour.Iʼmnotsayingwhatotherpeopledo.ItʼsfinethatotherpeoplewanttothinkaboutPoincaréconjectureindimensionfour.Great.Forme,therearejustmanythingsIliketothinkabout.Othersubjects,notjusttopology.Theworldofmathematicsisverybig.DimensionfourPoincaréconjectureisanimportantpart,butjustonepart.YanZou,seniorstudent:Whatdoyouthinkaboutthecomplexdynamics?Smale:Idonʼtknowsomuchincomplexdynamics.Likephaseʼsproblem,thethesisincomplexdynamics.Itis1970s,fortyyearsago,thatthecomplexdynamicswasattheverybeginning.Therearesomeveryhardproblemsandmanybeautifulthingsconnected.Inbinomialdynamics,especially.Itʼsaverybeautifulsubject.Itcanbemathematicallyadifferentnewland.Iʼmveryenthusiasticaboutcomplexdynamics,butitisnotimmediatelyapplicabletotherealworlddynamics.YueYu,juniorstudent:Therearealotofapplicationsofdifferentialtopologyineconomicsorotherrelatedareas.Aretheyreallyprofoundapplicationsofmathematicsorjustsomedefinitionsborrowedfrommathematics?Prof.Smale:Iwouldsaysomeareinbetween.Iworkedineconomicsin1970s.Myfeelingaboutmycontributionwastogiveafoundationtotheeconomicsequilibriumtheory.Idonotusedeepresultsfromdifferentialtopology,butsomeresults,andgivedifferentperspectivesontheequilibriumtheory.YueYu,juniorstudent:Werethoseapplicationsalsocontributenewthingstomathematicsitself?Prof.Smale:Well,certainlyeconomicstheoryhascontributedtomathematics,especiallygametheory,likemathematicprogramminghaspartlyinfluencedbyeconomics.Thereissomefeedback,theoptimization.Yeah,thereisquitealot.Prof.LanWen:DoyouknowthatSmalehasaverybigcollectionofcrystals?Heisalsoaprofessionalphotographer.Iʼmwonderingwhyhewouldspendhisvaluabletimeoncollections.Doesitwastemuchtime?Prof.Smale:Ianswerareversequestion.WhydoIspendmyvaluabletimeonmathematics?IdonʼtneedtobecauseIhaveagoodincome.Crystalsareworthmoreintermsofmoney,somaybeIamlosingmoneywhenpeopleappreciatethemineralsmorethanmymathematics.MaybeIshouldnotbedistractedbymathematicsorothersciences.Itrytokeepsomebalance.Prof.LanWen:Whatisthemostimportantthingforastudent,hard-workingortalent?Theyaretwoextremes.Traditionalchineseseemtoappreciatemoreahard-workingtype,whatisyouropinion?Prof.Smale:Iamnotahard-workingtype,butIknowitisgoodtoworkhardsometimes.Onehastothinkaboutwhatoneisdoing.WhatamIdoinginmywholelife?WhatamIdoinginmathematics?Idothisallthetimenow.ThenIjuststop,sitbackandthinkwhatisgoingon.EverymorningwhenIwakeup,IwouldmakeakindoflistofthingsIshouldpayattentionthatdayorthenextday.ThenItriedtoprioritizewhicharemoreimportant,whichshouldIdofirst.ThenIhavetothinkwhatamIdoingandhowamIgoingtodoit.Spendmoretimeonmathematicsorminerals?Ispendahugeamountoftimeonhealth.Aftermineralsandmathematicsmyhealthcomesfirst.SoIdoalotofresearchesonmedicinesandhealth,asitrelatestomyownhealth.Itakefiftypillsaday,likevitaminBorC.Thentheresearchcomesin.AndIchangethepills.Removesome,ormaybeaddsome.IanalyzewhatshouldIbeeatingtobehealthy,whatotherthingsshouldIusetobehealthy.Ihadbloodtestfrequentlyjusttoseehowmybodyisdoing.Soyouseeminerals,mathematic,health.Isaymathematicsisabroadsense,itʼsnotjustmathematics.Imyselfisactuallynotamathematician.Iʼmamathematicalscientist.SoINotaMathematician,ButaMathematicalScientistSteveSmale070809416Smale1114HodgeTheory→2122010.4/0908——809068125131——/09300“”“”——“”“”“”——·“-”——•094170909cs•418wiseuwiseu122010.434161560“”PPT“”“”“”“”“”64“”“”“”1409411715608730PPT“”“”“”2009-201072909“”——4171560050607wanttoseemathematicsinthesenseof,especially,whatishappeningintheworld.Engineering,statisticsandpsychology.Ithinkmathematicsareoftenfoundationsfortheseareas.Sothatrequiresalookingin,notjustmathematics,butmathematicalsciences.Mathematichaschangedahugeamountinthelast30or40years.Biologicalscience,computerscience,computationsciencehavechangedthefaceofmathematics.Iʼmtalkingtoomuch.Prof.LanWen:Iguessthatwhenyouwereyoung,youarenotonlyinterestedinmathematics.Iʼmwonderingthatinyourundergraduateyears,howdidyoudecidetodevoteyourselftoma