黎曼猜想淺說

發布日期:2019-10-17

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2000 NIAN 5 YUE 24 RI, MEIGUOKELEISHUXUEYANJIUSUO (Clay Mathematics Institute) ZAIFAGUOBALIZHAOKAILEYICISHUXUEHUIYI。 ZAIHUIYISHANG, YUHUIZHEMENLIECHULEQIGESHUXUENANTI, BINGZUOCHULEYIGEPOJUHONGDONGXINGDEJUEDING: WEIMEIGENANTISHELI 100 WANMEIYUANDEJUEJIANGJIN。 JUCICIHUIYI 100 NIANQIANDE 1900 NIAN, YESHIZAIBALI, YESHIZAIYICISHUXUEHUIYISHANG, YIWEIMINGJIAOXIERBOTE (David Hilbert) DEDEGUOSHUXUEDASHIYELIECHULEYIXILIESHUXUENANTI。 NEIXIENANTIYIFENQIANDEJIANGJINDOUMEIYOU, DANDUIHOUSHIDESHUXUEFAZHANCHANSHENGLESHENYUANYINGXIANG。 ZHELIANGCIYUANGEYIGESHIJIYAOXIANGHUYINGDESHUXUEHUIYICHULEDOUZAIBALIZHAOKAIWAI, HUANYOUYIGEGONGTONGZHICHU, NEIJIUSHIZAISUOLIECHUDENANTIZHIZHONG, YOUYIGE——BINGQIEZHIYOUYIGE——SHIGONGTONGDE。

NEIGENANTIJIUSHI “LIMANCAIXIANG” (Riemann hypothesis)。

LIMANCAIXIANGGUMINGSIYI, SHIYOUYIWEIMINGJIAOLIMAN (Bernhard Riemann) DESHUXUEJIATICHUDE, NEIWEISHUXUEJIAYU 1826 NIANCHUSHENGZAIRUJINSHUYUDEGUO, DANGSHISHUYUHANNUOWEIWANGGUO (Kingdom of Hanover) DEYIZUOMINGJIAOBULIESILUNCI (Breselenz) DEXIAOZHEN。 1859 NIAN, LIMANBEIXUANWEILEBOLINKEXUEYUANDETONGXINYUANSHI。 ZUOWEIDUIZHEYICHONGGAORONGYUDEHUIBAO, TAXIANGBOLINKEXUEYUANTIJIAOLEYIPIANTIWEI “LUNXIAOYUGEIDINGSHUZHIDESUSHUGESHU” DELUNWEN。 NEIPIANZHIYOUDUANDUANBAYEDELUNWENJIUSHILIMANCAIXIANGDE “DANSHENGDI”。

LIMANNEIPIANLUNWENSUOYANJIUDESHIYIGESHUXUEJIAMENCHANGQIYILAIJIUHENGANXINGQUDEWENTI, NEIJIUSHISUSHUDEFENBU。 SUSHUSHIXIANG 2、 5、 19、 137 NEIYANGCHULE 1 HEZISHENYIWAIBUNENGBEIQITAZHENGZHENGSHUZHENGCHUDESHU。 ZHEXIESHUZAISHULUNYANJIUZHONGYOUZHUJIDADEZHONGYAOXING, YINWEISUOYOUDAYU 1 DEZHENGZHENGSHUDOUKEYIBIAOSHICHENGTAMENDECHENGJI。 CONGMOUZHONGYIYISHANGJIANG, TAMENZAISHULUNZHONGDEDIWEILEISIYUGOUZHUWANWUDEYUANZIZAIWULISHIJIEZHONGDEDIWEI。 SUSHUDEDINGYIJIANDANDEKEYIZAIZHONGXUE、 SHENZHIXIAOXUEKESHANGJINXINGJIANGSHOU, DANTAMENDEFENBUQUEAOMIAODEYIHUXUNCHANG, SHUXUEJIAMENFUCHULEJIDADEXINLI, QUEQIJINWEINENGCHEDILEJIE。 LIMANNEIPIANLUNWENDEYIGEZHONGDACHENGGUO, JIUSHIFAXIANSUSHUFENBUDEAOMIWANQUANYUNZANGLEZAIYIGETESHUDEHANSHUZHIZHONG——YOUQISHI, SHINEIGEHANSHUQUZHIWEILINGDEYIXILIETESHUDEDIANDUISUSHUFENBUDEXIZHIGUILVYOUZHUJUEDINGXINGDEYINGXIANG。 NEIGEHANSHURUJINBEICHENGWEILIMAN ζ HANSHU, NEIYIXILIETESHUDEDIANZEBEICHENGWEILIMAN ζ HANSHUDEFEIPINGFANLINGDIAN (XIAWENZHONGYOUSHIJIANGJIANCHENGQIWEILINGDIAN)。

YOUYISIDESHI, LIMANNEIPIANLUNWENDECHENGGUOSUIRANZHONGDA, WENZIQUEJIWEIJIANLIAN, SHENZHIJIANLIANDEYOUXIEGUOFEN, YINWEITABAOKUOLEHENDUO “ZHENGMINGCONGLVE” DEDIFANG。 ERYAOMINGDESHI, “ZHENGMINGCONGLVE” YUANBENSHIGAIYONGLAISHENGLVENEIXIEXIANERYIJIANDEZHENGMINGDE, LIMANDELUNWENQUEBINGFEIRUCI, TANEIXIE “ZHENGMINGCONGLVE” DEDIFANGYOUXIEHUAFEILEHOUSHISHUXUEJIAMENJISHINIANDENULICAIDEYIBUQUAN, YOUXIESHENZHIZHIDAOJINTIANRENGSHIKONGBAI。

LIMANWEISHENMEYAOBANEIMEDUOBINGFEIXIANERYIJIANDEZHENGMINGCONGLVENI? WOMENWUFAQUEZHI, YEXUSHIYINWEITAMENDUIYUTALAISHUOQUESHISHIXIANERYIJIANDE, YEXUSHIYINWEIBUXIANGHUATAIDUOSHIJIANLAIZHUANXIEWENZHANG。 DANYOUYIDIANJIBENKEYIQUEDING, NEIJIUSHITADE “ZHENGMINGCONGLVE” JUEBUSHILEISIYUDIAOPIXUESHENGMENGHUNKAOSHIDEZUOFA, ERQIEHENKENENGYEBINGBUSHIBACUOWUZHENGMINGDANGCHENGZHENGQUEDEMANGMULEGUAN——HOUZHEZAISHUXUESHISHANGBUFAXIANLI, BIRUFAGUOSHUXUEJIAFEIMA (Pierre de Fermat) ZAIXIEXIAFEIMACAIXIANGSHISUOBIAOSHIDE “WOFAXIANLEYIGEZHENZHENGCHUSEDEZHENGMING,KEXIYEBIANTAIZHAIXIEBUXIALAI” JIUJIBENYIBEISHUXUEJIERENDINGSHIBACUOWUZHENGMINGDANGCHENGZHENGQUEDEMANGMULEGUAN。 YINWEIRENMENHOULAICONGLIMANDESHOUGAOZHONGFAXIANTADUIXUDUOLUNWENZHONGCONGLVELEDEZHENGMINGSHIZUOGUOZHASHIYANJIUDE, ERQIENEIXIEYANJIUDESHUIPINGZHIGAO, SHENZHIZAIGELEJISHINIANZHIHOUBEIZHENGLICHULAISHI, YOUSHIYERENGJUYOUJIDADELINGXIANXING。

DANLIMANDELUNWENZAIWEISHUBUSHAODE “ZHENGMINGCONGLVE” ZHIWAI, QUEYINRENZHUMUDIBAOHANLEYIGETAMINGQUECHENGRENZIJIWUFAZHENGMINGDEMINGTI, NEIGEMINGTIJIUSHILIMANCAIXIANG。

NEIME, LIMANCAIXIANGJIUJINGSHIYIGESHENMECAIXIANGNI? JIANDANDISHUO, SHIYIGEGUANYUWOMENQIANMIANTIDAODE, DUISUSHUFENBUDEXIZHIGUILVYOUZHUJUEDINGXINGYINGXIANGDELIMAN ζ HANSHUDEFEIPINGFANLINGDIANDECAIXIANG。 GUANYUNEIXIEFEIPINGFANLINGDIAN, RONGYIZHENGMINGDEJIEGUOZHIYOUYIGE, NEIJIUSHITAMENDOUFENBUZAIYIGEDAIZHUANGQUYUSHANG, DANLIMANRENWEITAMENDEFENBUYAOBIZHEGERONGYIZHENGMINGDEJIEGUOQIZHENGDEDUO, TACAICETAMENQUANDOUWEIYUGAIDAIZHUANGQUYUZHENGZHONGYANGDEYITIAOZHIXIANSHANG, ZHEJIUSHISUOWEIDELIMANCAIXIANG。 ERZHETIAOBEICAICEWEIBAOHANLIMAN ζ HANSHUSUOYOUFEIPINGFANLINGDIANDEZHIXIANZEBEICHENGWEILINJIEXIAN。

ER

LIMANCAIXIANGZI 1859 NIAN “DANSHENG” YILAI, YIJINGGUOLEYIBAIWUSHIDUOGECHUNQIU。 ZAIZHEQIJIAN, TAJIUXIANGYIZUOWEIEDESHANFENG, XIYINLEWUSHUSHUXUEJIAQIANQUPANDENG, QUESHUIYEMEINENGDENGDING。 DANGRAN, RUGUOJINCONGSHIJIANSHANGBIJIAODEHUA, LIMANCAIXIANGDEZHEGEJILUGENFEIMACAIXIANGSHIGESANGEBANSHIJIYISHANGCAIBEIJIEJUE, YIJIGEDEBAHECAIXIANGLIJINGLIANGGEBANSHIJIYISHANGRENGYILIBUDAOXIANGBI, HUANCHADEHENYUAN。 DANLIMANCAIXIANGZAISHUXUESHANGDEZHONGYAOXINGQUEYAOYUANYUANCHAOGUOZHELIANGGEDAZHONGZHIMINGDUGENGGAODECAIXIANG。 YOURENTONGJIGUO, ZAIDANGJINSHUXUEWENXIANZHONGYIYOUCHAOGUOYIQIANTIAOSHUXUEMINGTIYILIMANCAIXIANG (HUOQITUIGUANGXINGSHI) DECHENGLIWEIQIANTI。 ZHEYIWEIZHU: RUGUOLIMANCAIXIANGJIQITUIGUANGXINGSHIBEIZHENGMING, SUOYOUNEIXIESHUXUEMINGTIJIUQUANDOUKEYIRONGSHENGWEIDINGLI; FANZHI, RUGUOLIMANCAIXIANGBEIFOUZHENG, ZENEIXIESHUXUEMINGTIZHONGQIMAYOUYIBUFENKONGJIANGCHENGWEIPEIZANG。 YIGESHUXUECAIXIANGYUWEISHURUCIZHONGDUODESHUXUEMINGTIDEMINGYUNXIXIXIANGGUAN, SHIJIWEIHANYOUDE。

BUGUO, SHUXUEJIAMENPANDENGLIMANCAIXIANGZHEZUOWEIESHANFENGDENULISUIQIJINWEINENGQUDEWANQUANCHENGGONG, ZAIZHEGUOCHENGZHONGQUEYEQUDELEYIXIEJIEDUANXINGCHENGGUO, HAOBISHIZHAXIALEJIZUOYINGZHAI。

ZHEQIZHONGDIYIGEJIEDUANXINGCHENGGUOCHUXIANZAILIMANCAIXIANGWENSHI 37 NIANHOUDE 1896 NIAN。 WOMENZAIQIANMIANTIDAOGUO, GUANYULIMAN ζ HANSHUDEFEIPINGFANLINGDIAN, RONGYIZHENGMINGDEJIEGUOZHIYOUYIGE, NEIJIUSHITAMENDOUFENBUZAIYIGEDAIZHUANGQUYUSHANG。 NEIGEJIEDUANXINGCHENGGUOSHISHENMENI? JIUSHIJIANGNEIGEDAIZHUANGQUYUDEBIANJIETICHUDIAOLE——YEJIUSHISHUO, LIMAN ζ HANSHUDEFEIPINGFANLINGDIANZHIFENBUZAINEIGEDAIZHUANGQUYUDENEIBU, ERBUBAOKUOBIANJIE。 ZHEGECHENGGUOSHIYOUFAGUOSHUXUEJIAHADAMA (Jacques Hadamard) YUBILISHISHUXUEJIAPUSEN (Charles de la Vallée-Poussin) BICIDULIDIQUDEDE。

CUKANQILAI, ZHESIHUSHIHENWEIBUZUDAODECHENGGUO, YIGEDAIZHUANGQUYUDEBIANJIEGENTADENEIBUXIANGBI, CONGMIANJISHANGJIANGBILISHIJISHANGSHILING。 DANSHIBIEXIAOKANLEZHEGECHENGGUO, TADUIYUYANJIULIMANCAIXIANGLAISHUOZHISHIYIXIAOBU, DUIYUYANJIULINGYIGESHUXUECAIXIANGLAISHUOQUESHIJUDADEFEIYUE, YINWEITAZHIJIEDAOZHILEHOUZHEDEZHENGMING。 NEIGESHUXUECAIXIANGRUJINYIBEICHENGWEISUSHUDINGLI (prime number theorem), TASUOMIAOSHUDESHISUSHUDEDAFANWEIFENBUGUILV。 SUSHUDINGLIZIBEITICHUYILAIXUANERWEIJUEYICHAOGUOYIBAINIAN, ZAIDANGSHINAISHIYIGEBILIMANCAIXIANGGENGLINGSHUXUEJIEQIDAIDEDONGXI。

ZAISHANGSHUCHENGGUOZHIHOUYOUGELE 18 NIAN, 1914 NIAN, DANMAISHUXUEJIABOER (Harald Bohr) YUDEGUOSHUXUEJIALANDAO (Edmund Landau) QUDELELINGYIGEJIEDUANXINGCHENGGUO, NEIJIUSHIZHENGMINGLELIMAN ζ HANSHUDEFEIPINGFANLINGDIANQINGXIANGYU “JINMITUANJIE” ZAILINJIEXIANDEZHOUWEI。 ZHEGEJIEGUOYONGSHUXUEYUYANLAISHUO, JIUSHIBAOHANLINJIEXIANDEWULUNDUOMEZHAIDEDAIZHUANGQUYUDOUBAOHANLELIMAN ζ HANSHUDEJIHUSUOYOUDEFEIPINGFANLINGDIAN。 BUGUO “JINMITUANJIE” GUI “JINMITUANJIE”, ZHEYIJIEGUOQUEBUZUYIZHENGMINGRENHEYIGELINGDIANQIAHAOJIUZAILINJIEXIANSHANG, YINCITAJULILIMANCAIXIANGDEYAOQIURENGRANXIANGCHAHENYUAN。

DANJIUZAINEITONGYINIAN, LINGYIGEJIEDUANXINGCHENGGUOCHUXIANLE: YINGGUOSHUXUEJIAHADAI (Godfrey Hardy) ZHONGYUJIANG “HONGQI” CHASHANGLELINJIEXIAN——TAZHENGMINGLELIMAN ζ HANSHUYOUWUQIONGDUOGEFEIPINGFANLINGDIANWEIYULINJIEXIANSHANG。 CUKANQILAI, ZHESIHUSHIYIGEFEITONGXIAOKEDEJIEGUO, YINWEILIMAN ζ HANSHUDEFEIPINGFANLINGDIANZONGGONGJIUSHIWUQIONGDUOGE, ERHADAIZHENGMINGLEYOUWUQIONGDUOGELINGDIANWEIYULINJIEXIANSHANG, CONGZIMIANSHANGKAN, LIANGZHEYIJINGYIMOYIYANGLE。 KEXIDESHI, “WUQIONG” NAISHISHUXUEZHONGYIGEHENWEIMIAODEGAINIAN, TONGYANGSHIWUQIONG, BICIQUEWEIBISHIYIHUISHI, BUJINWEIBISHIYIHUISHI, JIANZHIKEYIYAOCHADUOYUANJIUCHADUOYUAN, SHENZHICHAWUQIONGYUAN! YINCI, WEILEZHIDAOHADAIDEJIEGUOLILIMANCAIXIANGDEYAOQIUHUANYOUDUOYUAN, WOMENXUYAOGENGJUTIDEJIEGUO。

NEIYANGDEJUTIJIEGUOCHUXIANZAI 7 NIANHOUDE 1921 NIAN。 NEIYINIAN, HADAIYUYINGGUOSHUXUEJIALITEWUDE (John Littlewood) HEZUO, DUIZIJI 7 NIANQIANNEIGEJIEGUOZHONGDE “WUQIONG” ZUOCHULEJUTIGUJI。 NEIME, ANZHAOTAMENDEJUTIGUJI, NEIYIBEIZHENGMINGWEIWEIYULINJIEXIANSHANGDE “WUQIONGDUOGEFEIPINGFANLINGDIAN” GENQUANBUFEIPINGFANLINGDIANXIANGBI, JIUJINGZHANDUODADEBAIFENBINI? DAANKENENGJUSANGDECHUHUDUZHEMENDEYILIAO: BAIFENZHILING!

SHUXUEJIAMENJIANGZHEGEBAIFENBITUIJINDAOYIGEDAYULINGDESHUZISHIZAI 21 NIANHOUDE 1942 NIAN。 NEIYINIAN, NUOWEISHUXUEJIASAIERBOGE (Atle Selberg) ZHONGYUZHENGMINGLEZHEGEBAIFENBIDAYULING。 SAIERBOGEZUOCHUZHEXIANGCHENGGUOSHIZHENGZHIDIERCISHIJIEDAZHANDEXIAOYANZAIOUZHOUGEDIMIMAN, TASUOZAIDENUOWEIAOSILUDAXUEJIHUCHENGLEYIZUOGUDAO, LIANSHUXUEQIKANDOUWUFASONGDA。 DANSAIERBOGEBINGBUZAIHU, TABIAOSHI “ZHEJIUXIANGCHUZAIYIZUOJIANYULI, NIYUSHIGEJUELE, DANNIXIANRANYOUJIHUIBAZHUYILIJIZHONGZAIZIJIDEXIANGFASHANG, ERBUHUIYINQITARENDESUOZUOSUOWEIERFENXIN, CONGZHEGEYIYISHANGJIANGWOJUEDENEIZHONGQINGXINGDUIYUWODEYANJIULAISHUOYOUXUDUOYOULIDEFANGMIAN”。 SAIERBOGEHENHAODILIYONGLENEI “XUDUOYOULIDEFANGMIAN”, GUDUDIJINXINGZHU “YIGERENDEZHANDOU”, BINGZUIZHONGQUDELECHENGGUO, TADECHENGGUOSHIRUCIXIANZHU, YIZHIYUBOERZAIZHANHOUCENGXICHENGSHUOZHANSHIZHENGGEOUZHOUDESHUXUEXINWENKEYIGUIJIEWEIYIGECI, NEIJIUSHI: SAIERBOGE。

BUGUOSAIERBOGESUIRANZHENGMINGLENEIGEBAIFENBIDAYULING, QUEBINGMEIYOUZAILUNWENZHONGGEICHUJUTISHUZHI。 ZAISAIERBOGEZHIHOU, SHUXUEJIAMENKAISHIDUIZHEYIBILIDEJUTISHUZHIJINXINGYANJIU, QIZHONGYIMEIGUOSHUXUEJIALIEWENSEN (Norman Levinson) DECHENGGUOZUIWEIXIANZHU, TAZHENGMINGLEZHISHAOYOU 34% DELINGDIANWEIYULINJIEXIANSHANG。 LIEWENSENQUDEZHEYICHENGGUOSHIZAI 1974 NIAN, NEISHITAYINIANGUOHUAJIA, BINGQIEXINGJIANGZOUDAOSHENGMINGDEJINTOU (TADIERNIANJIUQUSHILE), QUEYIRANWANQIANGDICONGSHIZHUSHUXUEYANJIU。 ZAILIEWENSENZHIHOU, ZHEFANGMIANDETUIJINBIANDESHIFENHUANMAN, JIWEISHUXUEJIAFEIJINJIUNIUERHUZHILIYEZHINENGZAIBAIFENBIDEDIERWEISHUZISHANGZUOWENZHANG, QIZHONGBAOKUOZHONGGUOSHUXUEJIALOUSHITUOYUYAOQI (TAMENYU 1980 NIANZHENGMINGLEZHISHAOYOU 35% DELINGDIANWEIYULINJIEXIANSHANG)。 ZHIDAO 1989 NIAN, CAIYOURENHANDONGBAIFENBIDEDIYIWEISHUZI: MEIGUOSHUXUEJIAKANGRUI (Brian Conrey) ZHENGMINGLEZHISHAOYOU 40% DELINGDIANWEIYULINJIEXIANSHANG。 ZHEYESHIZHEFANGMIAN——BINGQIEYESHIZHENGGELIMANCAIXIANGYANJIUZHONG——ZUIQIANGDEJIEGUOZHIYI, ZHEFANGMIANDENULIRENGZAIJIXU。

LINGWAIZHIDEYITIDESHI, “LIMANCAIXIANG” ZHEYIJINZIZHAOPAIHOULAIBEITUIERGUANGZHI, YONGLAIBIAOSHIYIXIE “SHANZHAIBAN” HE “HAOHUABAN” DECAIXIANG。 NEIXIECAIXIANGWEISHENMENENGGENLIMANCAIXIANGGONGXIANGZHAOPAINI? YINWEITAMENGENLIMANCAIXIANGYOUJIDADEXIANGSIXING, BIRUDOUYOUYIGEGENLIMAN ζ HANSHUXIANGLEISIDEHANSHU, NEIGEHANSHUJUYOUYULIMAN ζ HANSHUXIANGLEISIDEXINGZHI, DENGDENG。 ZAINEIXIECAIXIANGZHONG, “HAOHUABAN” LIMANCAIXIANGNAISHIYIXIEBILIMANCAIXIANGGENGQIANGDECAIXIANG (JISHANGWENTIDAOGUODELIMANCAIXIANGDETUIGUANGXINGSHI), TAMENGENLIMANCAIXIANGYIYANG, QIJINSHANGWEIDEDAOZHENGMING (ZHESHIXIANRANDE, FOUZEDEHUALIMANCAIXIANGZUOWEIQITELIYEJIUBEIZHENGMINGLE); “SHANZHAIBAN” LIMANCAIXIANGZESHIGENLIMANCAIXIANGYOUXIANGSIXINGQUEHUBUBAOHANDECAIXIANG, TAMENYIQUANBUDEDAOLEZHENGMING, ERQIEPIEKAIWOMENSUOQUBUZHONGTINGDECHUOHAOBULUN, TAMENDEZHENGMINGNAISHISHUXUESHANGDEZHONGDACHENGGUO, JICUISHENGGUOXINSHUXUEFANGFADEDANSHENG, YEWEIZHENGMINGZHEZHAIQUGUOSHUXUEJIEDEZUIGAOJIANG——FEIERCIJIANG (Fields medal)。 ERQIE, “SHANZHAIBAN” LIMANCAIXIANGZUOWEIWEIYIGUAZHULIMANCAIXIANGZHEYIJINZIZHAOPAIQUEBEIZHENGMINGLEDECAIXIANG, CENGSHIRENMENDUIJIUGONGBUXIADELIMANCAIXIANGYEYIDULEGUANQILAI。 KEXITASHANZHISHI, BINGBUZONGSHIKEYIGONGYUDE。 CONGMUQIANDEQINGKUANGLAIKAN, “SHANZHAIBAN” LIMANCAIXIANGJIUZHINENGZAI “SHANZHAI” LIWANWAN, TAMENDEZHENGMINGSUIRANZHONGYAO, DUIYUJIEJUEZHENZHENGDELIMANCAIXIANGQUEBINGWUSHIZHIXINGDEQISHI。

SAN

LIAOLEZHEMEDUOGUANYULIMANCAIXIANGDEYANJIUCHENGGUO, WOMENSHAOSHAOHUANHUANKOUWEI, LAILIAOYIXIESHUXUEJIADEGUSHIBA。 YEXUZAIHENDUORENYANLI, SHUXUESHIYIMENHENKUZAODEXUEWEN, SHUXUEJIAMENZESHIYIQUNXINGGEFAWEIDEGUAIREN。 DANSHIJISHANG, FUYOUZHIHUIDERENWANGWANGSHIBUHUIZHENZHENGFAWEIDE, SHUXUEJIAMENYESHIRUCI, TAMENZAIMAITOUYANSUANDEQINKENZHIWAI, YEGEIWOMENLIUXIALEXUDUODUTEDEYOUMO。

XIONGYALISHUXUEJIABOLIYA (George Pólya) CENGJINGJIANGGUOYIGEGENLIMANCAIXIANGYOUGUANDEXIAOGUSHI, GUSHIDEZHUJIAOJIUSHIWOMENQIANMIANTIDAOGUODEYINGGUOSHUXUEJIAHADAIYUDANMAISHUXUEJIABOER。 ZHELIANGWEIZAILIMANCAIXIANGYANJIUZHONGZUOCHUGUOCHENGGUODESHUXUEJIADANGRANDOUDUILIMANCAIXIANGHUAIYOUNONGHOUDEXINGQU。 YOUYIDUANSHIJIAN, HADAICHANGCHANGLIYONGJIAQIFANGWENBOER, YIQITAOLUNLIMANCAIXIANG, ZHIDAOJIAQIJIANGJINCAICONGCONGGANHUIYINGGUO。 JIEGUOYOUYICI, DANGHADAIYOUBIXUCONGCONGGANHUIYINGGUOSHI, HENBUXINGDIFAXIANMATOUSHANGZHISHENGXIAYITIAOXIAOCHUANKEYICHENGZUOLE。 CONGDANMAIDAOYINGGUOYAOKUAYUEJIBAIGONGLIKUANDEBEIHAI (North Sea), ZAIDAHAIZHONGCHENGZUOXIAOCHUANKEBUSHINAOZHUWANDESHIQING, NONGBUHAOJIUDEZANGSHENYUFU。 WEILELVTUDEPINGAN, XINFENGSHANGDIDECHENGKEMENDADOUMANGZHUQIQIUSHANGDIDEBAOYOU。 HADAIQUESHIYIGEJIANJUEBUXINSHANGDIDEREN, FEIDANBUXIN, SHENZHIHUANXUYIGENSHANGDIZUODUI: BAXIANGDAZHONGZHENGMINGSHANGDIBUCUNZAILIERUZIJIMOUYINIANDENIANDUXINYUANZHIYI。 BUGUOZAINEISHENGSIYOUGUANDELVCHENGMIANQIANHADAIYEMEIXIANZHU, TAGEIBOERFAQULEYIZHANGJIANDUANDEMINGXINPIAN, SHANGMIANZHIXIELEYIJUHUA: “WOYIJINGZHENGMINGLELIMANCAIXIANG”。 HADAIGUOZHENZHENGMINGLELIMANCAIXIANGMA? DANGRANBUSHI。 TAWEISHENMEYAOFAZHEMEYIZHANGHUYOUTONGSHIDEMINGXINPIANNI? DANGTAPINGANDIDAYINGGUOHOUTAXIANGBOERJIESHILEYUANYIN。 TASHUORUGUONEICITASUOCHENGZUODEXIAOCHUANGUOZHENCHENMEILEDEHUA, NEIJUHUAJIUHUIBIANDESIWUDUIZHENG, RENMENJIUZHIHAOXIANGXINTAQUESHIZHENGMINGLELIMANCAIXIANG。 KESHITAZHIDAOSHANGDISHIJUEBUHUIGANXINRANGTAZHEYANGYIGEJIANJUEBUXINSHANGDIDERENHUODERUCIJUDADERONGYUDE, YINCITAYIDINGBUHUIRANGXIAOCHUANCHENMEIDE。

HADAIPINGJIEZIJIDEYOUMOCHENGWEILEGUSHIZHUJIAO, YOUXIESHUXUEJIAZESHIYINWEIQITASHUXUEJIADEYOUMOERBEIDONGDICHENGWEILEGUSHIZHUJIAO, WOMENQIANMIANTIDAOGUODEFAGUOSHUXUEJIAHADAMAYUBILISHISHUXUEJIAPUSENJIUSHIRUCI。 ZHELIANGRENCHENGWEIZHUJIAODEYUANYINDAJIAKONGPASHICAIBUDAODE, NEISHIYINWEITAMENDECHANGSHOU: HADAMAXIANGNIAN 98 SUI, PUSENHUODAO 96 SUI。 ZHELIANGGELINGRENYANHONGDESUISHUBUZHICONGHESHIQIYINFALEYIGECHUANSHUO, NEIJIUSHI: SHUIYAOSHINENGZHENGMINGLIMANCAIXIANG, TAJIUNENGBUXIU——BUSHICHOUXIANGYIYISHANGDEBUXIU (NEISHIHAOWUYIWENDE), ERSHISHIJIYIYISHANGDEBUXIU (JICHANGSHENGBULAO)! BUGUOZHEGECHUANSHUODEPAOZHIZHEKANLAISHIMEIYOUGUANHUAIDAOBOERHELANDAO, TAMENDEYANJIUCHENGGUOKEBIHADAMAHEPUSENDECHENGGUOQIANGDUOLE, ZHAOSHUOQIMAYEGAIHUNGEBAISUILAORENDANGDANGBA。 JIEGUONI? LANDAOZHIHUOLE 61 SUI, BOERSHAOSHENGYICHOU, YEZHIYOU 63 SUI。 KENENGSHIYISHIDAOZHEGECHUANSHUOLOUDONGTAIDA, CHUSHENGYUBOLANDESHUXUEJIAOUDELIZIKE (Andrew Odlyzko) BAYOUMOZHIXIANGLELINGYIGEFANGXIANG, TICHULEYIGEWANQUANXIANGFANDESHUOFA, NEIJIUSHI: SHUIYAOSHIFOUZHENGLELIMANCAIXIANG, TAJIUHUILIKESIQU! OUDELIZIKESHENZHIKAIWANXIAOSHUOQISHILIMANCAIXIANGYIJINGBEIFOUZHENGLE, ZHIBUGUONEIGEFOUZHENGLELIMANCAIXIANGDEDAOMEIDANMEILAIDEJIFABIAOLUNWENJIUSIQULE。

DANGRAN, ZHEXIEDOUZHINENGZUOWEIFANHOUCHAYUDETANZIERBUYIJIAOZHEN。 BUGUO, YIGEJIDUJIANSHENDEDONGXIDUITOURUDEGUOYUSHENRUDERENCHANSHENGJIANKANGFANGMIANDEYINGXIANG, DAOBINGBUSHIHAOWUKENENGDE。 SHUXUEJIEYEQUESHIYOURENCAICE, LIMANCAIXIANGDEJIDUJIANSHENYOUKENENGDUIGEBIESHUXUEJIADEJIANKANGCHANSHENGGUOYINGXIANG。 BIRULIUXINGCHUANJI《MEILIXINLING》DEZHUJIAO、 MEIGUOSHUXUEJIANASHEN (John Nash) CENGZAI 20 SHIJI 50 NIANDAIHOUQIYANJIUGUOLIMANCAIXIANG, ZAINEIZHIHOUBUJIUJIUHUANSHANGLEJINGSHENFENLIEZHENG。 NASHENHUANBINGDEYUANYINYIBANRENWEISHICANYUJUNFANGGONGZUOYINZHIDEXINLIYALI, DANYEYOURENRENWEITAMAORANQUKENLIMANCAIXIANGNEIYANGDEJIANGUO, DUIQIBINGZHENGFAZHANYOUKENENGQIDAOGUOTUIBOZHULANDEZUOYONG。

LIMANCAIXIANGKEYISHUOSHIDANGJINSHUXUEJIEZUIZHONGYAO、 BINGQIESHISHUXUEJIAMENZUIQIDAIJIEJUEDESHUXUECAIXIANG。 MEIGUOSHUXUEJIAMENGGEMALI (Hugh Montgomery) CENGJINGBIAOSHI, RUGUOYOUMOGUIDAYINGRANGSHUXUEJIAMENYONGZIJIDELINGHUNLAIHUANQUYIGESHUXUEMINGTIDEZHENGMING, DUOSHUSHUXUEJIAXIANGYAOHUANQUDEJIANGHUISHILIMANCAIXIANGDEZHENGMING。 ZAITANSUOLIMANCAIXIANGDEGUOCHENGZHONG, HENDUOSHUXUEJIACENGJINGMANHUAIXINXIN, JIANJIANDIQUEBEITADEJIANSHENSUOZHENDONG, TAIDUZHUANWEILEBEIGUAN。 WOMENQIANMIANTIDAOGUODELITEWUDEJIUSHIYIGELIZI, DANGTAHUANSHIXUESHENGDESHIHOU, TADEDAOSHIJIUSUISHOUBALIMAN ζ HANSHUXIEGEILETA, RANGTALIYONGSHUJIASHIJIANYANJIUQILINGDIANWEIZHI。 CHUCHUMAOLUDELITEWUDEYEBUDANGHUISHIDILINGMINGERQU。 HOULAITAYUHADAIDAOYEGUOZHENZAIZHEFANGMIANZUOCHULECHENGGUO。 DANJIANJIANDI, TADETAIDUFASHENGLEBIANHUA, SHENZHIBIAOSHI: “JIARUWOMENNENGGOUJIANDINGDIXIANGXINZHEGECAIXIANGSHICUOWUDE, RIZIHUIGUODEGENGSHUSHIXIE”。 CENGJINGZAI “SHANZHAIBAN” LIMANCAIXIANGYANJIUSHANGZUOCHUGUOCHENGGUODEFAGUOSHUXUEJIAWEIYI (André Weil) YEYOUGUOLEISIDETAIDUZHUANBIAN。 DANGTAZAI “SHANZHAIBAN” LIMANCAIXIANGYANJIUSHANGZUOCHUCHENGGUOSHI, CENGJINGYUYIXIEQITARENYIYANGDUIJIEJUELIMANCAIXIANGRANQILEXINXIN, HUANBIAOSHIRUGUOZIJIZHENGMINGLELIMANCAIXIANG, HUIGUYITUICHIDAOCAIXIANGTICHU 100 ZHOUNIAN (JI 1959 NIAN) SHICAIGONGBU——YANXIAZHIYI, ZIJIBUCHIYU 1959 NIANJIUYOUKENENGJIEJUELIMANCAIXIANG。 BUGUO, SUIYUEJIANJIANMOQULETADELEGUAN, TAWANNIANSHICENGDUIYIWEIYOURENCHENGREN, ZIJIYOUSHENGZHINIANBUTAIKENENGKANDAOLIMANCAIXIANGDEJIEJUE。 JIULIANBENWENKAITOUTIDAODENEIWEIDEGUOSHUXUEDASHIXIERBOTE, TADUILIMANCAIXIANGDEKANFAYEJINGLILECONGLEGUANDAOBEIGUANDEZHUANBIAN。 ZAI 1919 NIANDEYICIYANJIANGZHONG, XIERBOTECENGBIAOSHIZIJIYOUWANGJIANDAOLIMANCAIXIANGDEJIEJUE, DANHOULAITADETAIDUXIANZHUDIZHUANWEILEBEIGUAN。 JUSHUOYOURENCENGJINGWENTA: RUGUOTANENGZAI 500 NIANHOUZHONGFANRENJIAN, TAZUIXIANGWENDEWENTISHISHENME? TAHUIDASHUOSHI: SHIFOUYIJINGYOURENJIEJUELELIMANCAIXIANG?

JIEXIALAI, WOMENJIANGJIESHAORENMENCONGLINGYIGEFANGXIANGTANSUOLIMANCAIXIANGDEGUSHI, WOMENJIANGHUIKANDAO, NEILIBUJINYEYOUGUSHI, ERQIEHUANYOUYIXIEFEICHANGCHURENYILIAODEDONGXI。

SI

LIMANNEIPIANTICHULELIMANCAIXIANGDEZHUMINGLUNWENCHULEYOUXUDUO “ZHENGMINGCONGLVE” DEDIFANGWAI, HUANYOUYIGEHENTUCHUDETEDIAN, NEIJIUSHITASUIRANFANFUSHEJILELIMAN ζ HANSHUDEFEIPINGFANLINGDIAN, SHENZHIHUANTICHULEYULINGDIANFENBUYOUGUANDEYIXILIEMINGTI (BAOKUODAMINGDINGDINGDELIMANCAIXIANG), QUEMEIYOUJUCHUNAPAYIGEJUTIDELIZI——JIMEIYOUGEICHUNAPAYIGELINGDIANDESHUZHI。 ERQIEYUNEIXIE “ZHENGMINGCONGLVE” DEDIFANGBINGFEIRONGYIZHENGMINGTONGYANGYAOMINGDESHI, LIMANBUCENGGEICHUDENEIXIELINGDIANDESHUZHIYEBINGFEIQINGYIJIUNENGJISUANDELEDE。 SHISHISHANG, ZHIDAOLIMANNEIPIANLUNWENFABIAO 44 NIANHOUDE 1903 NIAN, CAIYOURENTIANBULEZHEFANGMIANDEKONGBAI: DANMAISHUXUEJIAGELANMU (G?rgen Gram) JISUANCHULE 15 GELINGDIANDESHUZHI。 ZHESHIRENMENSHOUCIKUISHIDAOLIMAN ζ HANSHUFEIPINGFANLINGDIANDEJUTICUNZAI。 DANGRAN, NEI 15 GELINGDIANQUANDOUWEIYULIMANCAIXIANGSUOYUYANDELINJIEXIANSHANG。

YUWOMENZAI DIERJIE ZHONGJIESHAODELILUNYANJIUZHONGDECENGCENGTUIJINJIBENPINGXING, SHUXUEJIAMENJISUANLINGDIANDEMANCHANGZHENGTU, YECHENGXIANCHULECENGCENGTUIJINDETAISHI。 DANZHETUIJINGUOCHENGZAIQICHUYIDUANSHIJIANLIQUEXIANDEJIWEIHUANMAN, ZHIDAO 1925 NIAN, CAIJISUANCHULEQUQU 138 GELINGDIAN, ERQIEZAINEIZHIHOUXIANRULETINGDUN。 WEISHENMEHUIXIANRUTINGDUNNI? YUANYINHENJIANDAN, JIUSHIDANGSHIJISUANLINGDIANDEFANGFABIJIAOBENZHUO, ZHISHIJISUANLIANGGUOYUJUDA。 ERDANGSHIDEJISUANYOUQUANKAOSHOUGONG, LINGDIANSHUMUYIDUO, JISUANLIANGJIUDADAOLELINGRENNANYIYINGFUDECHENGDU。

JIRANSHIJISUANFANGFADEBENZHUOSHIJISUANXIANRULETINGDUN, NEIMEHENXIANRANDI, JISUANDEZHONGXINQIDONGXUYAOYOUXINDEJISUANFANGFA。 ZHEXINDEJISUANFANGFAZAI 7 NIANHOUDE 1932 NIANZHONGYU “CHUTU” LE——WOMEIYOUXIECUO, QUESHISHI “CHUTU”, YINWEITASHICONGZAOYIQUSHILEDELIMANDESHOUGAOZHONG “WA” CHULAIDE!

LIMANNEIGESHIDAIDEYIXIEZHUMINGSHUXUEJIAYOUYIGEJINTIANDESHUXUEJIAMENHENSHAOXIAOFANG、 JINTIANDEDUZHEHENNANLIJIEDETEDIAN, NEIJIUSHICHANGCHANGBUFABIAOZIJIDEYANJIUCHENGGUO。 YOUYUZHEGETEDIAN, NEIXIESHUXUEJIADESHOUGAOYOUZHUBIPUTONGMINGRENYONGPINSUOJUYOUDEDANCHUNDELIEQIJIAZHIZHONGYAODEDUODEYIYI, YINWEICONGZHONGYOUKENENGFAXIANYIXIETAMENWEICENGFABIAOGUODEYANJIUCHENGGUO。 LIMANDESHOUGAOJIUSHIRUCI。 BUGUOLINGRENWANXIDESHI, LIMANDESHOUGAOZAITAQUSHIHOUYOUHENDAYIBUFENBEITADEGUANJIAFUZHILEYIJU, ZHIYOUYIXIAOBUFENBEITAQIZIQIANGJIULECHULAI。 ZAIJIEHOUYUSHENGDESHOUGAOZHONG, YOUYOUYIBUFENBEITAQIZIYISHEJISIRENXINXIWEIYOU “KEKOU” DIAOLE (QIZHONGBAOKUOXUDUOJIHUTONGPIANDOUSHISHUXUE, ZHIJIADAILEJISHAOLIANGSIRENXINXIDESHOUGAO), SHENGXIADECAISHIHOURENZHENZHENGKEYICHAYUEDE。 NEIXIEKEGONGCHAYUEDESHOUGAOBEISHOULUYUGETINGGENDAXUEDETUSHUGUAN。

BUGUO, NEIBUFENSHOUGAOSUIRANKEGONGCHAYUE, DANZHIYAOXIANGXIANGLIMANGONGKAIFABIAODEWENZHANGSHANGQIERUCIJIANSHEN, DONGZHEHUAFEIHOUSHISHUXUEJIAJISHINIANDESHIJIANCAINENGTIANBUKONGBAI, JIUBUNANXIANGXIANGYANDUTADESHOUGAOHUISHISHENMEGANJUELE。 LIMANDEYANJIULINGYUJIWEIKUANGUANG, SHOUGAOZHONGCHANGCHANGZHUBANLUNTIHUNZA, ERQIEJIHUMEIYOUBANJUSHUOMING。 ZILIMANDESHOUGAOBEICUNFANGYUGETINGGENDAXUETUSHUGUANYILAI, LUXUYOUYIXIESHUXUEJIAJISHUXUESHIXUEJIAMUMINGQIANQUYANJIU, DANZAINEIJIDUDEJIANSHENHUISEMIANQIAN, DADOUMANHUAIXIWANGERLAI, QUELIANGSHOUKONGKONGERQU。 LIMANDESHOUGAOJIUXIANGYIBENGAOMINGDEMIMABEN, LAOLAOSHOUHUZHUZHEWEIWEIDASHUXUEJIADESIWEIAOMI。

DANDAOLE 1932 NIAN, ZHONGYUYOUYIWEISHUXUEJIACONGLIMANDESHOUGAOZHONGHUODELEZHONGDAFAXIAN——FAXIANLIMANBUJINQINZIJISUANGUORUOGANGELINGDIANDESHUZHI, ERQIEHUANYOUZIJIDUTEDE、 ZHIDAO “CHUTU” ZHIRIRENGYAOYAOLINGXIANYUDANGSHISHUXUEJIEDEJISUANFANGFA。 ZHEYIFAXIANWEILIMAN ζ HANSHUFEIPINGFANLINGDIANDEJISUANDAILAILETUOTAIHUANGUBANDEBIANHUA, RANGTINGZHIZAIDI 138 GELINGDIANSHANGDEJISUANZHONGXINQIDONG。 DANGRAN, ZHEYIFAXIANYEJINYIBUTIGAOLELIMANNEIYUANBENJIUYIJIWEICHONGGAODESHENGWANG, ZAIHENDACHENGDUSHANGQUSANLEYIXIESHUXUEJIADUILIMANLUNWENZHONGNEIXIE “ZHENGMINGCONGLVE” BUFENDEHUAIYI。 YINWEITABIAOMINGLIMANNEIPIANGAODUJIANLIANDELUNWENZHISHIBINGSHANDEJIANDING, ZAINEIXIAMIANYOUZHUDALIANGZHASHIDEYANJIU。 NEIME, FAXIANZHEYIQIEDERENSHISHUINI? SHILIMANDEYIWEITONGBAO: DEGUOSHUXUEJIAXIGEER (Carl Ludwig Siegel)。 WEILECONGTIANSHUBANDELIMANSHOUGAOZHONG “CHUTU” GONGSHI, XIGEERFUCHULEJIANXINDENULI。 WEILEBIAOZHANGTADENULI, RENMENJIANGZHEYIJISUANLIMAN ζ HANSHUFEIPINGFANLINGDIANDEXINFANGFACHENGWEILELIMAN-XIGEERGONGSHI (Riemann–Siegel formula)。

LIMAN-XIGEERGONGSHIDE “CHUTU” DADATUIJINLELINGDIANJISUAN。 ZAIDUANDUANJINIANJIAN, SHUXUEJIAMENJIUBALINGDIANJISUANTUIJINLEYIGESHULIANGJI, DADAOLE 1000 GEYISHANGDELINGDIAN。 SUIRANSUIHOUBAOFADEDIERCISHIJIEDAZHANZHONGDUANLELINGDIANJISUAN, DANZHANHOUJISUANJIJISHUDEFAZHAN, YOUSHIDELINGDIANJISUANCHENGXIANCHULEJINGPENSHITOU: CONG 1956 NIANDAO 1969 NIANDESHIJINIANJIAN, BEIJISUANCHUDELINGDIANSHUMUYOUTUIJINLEHAOJIGESHULIANGJI, CONG 25,000 GETUIJINDAOLE 3,500,000 (350 WAN) GE。 DANGRAN, SUOYOUZHEXIELINGDIANYEDOUWUYILIWAIDIWEIYULIMANCAIXIANGSUOYUYANDELINJIEXIANSHANG。 SHUODAOZHELISHUNBIANTIXINGDUZHEYIXIA, WOMENZHELIJIXIAWENSUOSHUODELINGDIANJISUANCHUZAOQINEIXIEXIAOGUIMODEJISUANWAI, DADOUZHISHIYANZHENGLINGDIANSHIFOUZAILINJIEXIANSHANG, ERBINGBUJISUANTAMENDEJUTISHUZHI。

YANZHENGLE 350 WANGELINGDIANQUANBUWEIYULINJIEXIANSHANG, WUYIDADAZENGQIANGLESHUXUEJIAMENDUILIMANCAIXIANGDEXINXIN。 BUGUO, BUXIANGXINDEYEHUANSHIDAYOURENZAI。 BIRUDEGUOPULANGKESHUXUEYANJIUSUO (Max Planck Institute for Mathematics) DEYIWEIMINGJIAOCHAJIER (Don Zagier) DESHUXUEJIADUIZHEZHONGYANZHENGJIUBUYIWEIRAN。 ZAITAKANLAI, QUQU 350 WANGELINGDIANGENBENBUSHUOMINGWENTI。 TADEZHEZHONGBUYIWEIRANHENKUAIYUDAOLEDUISHOU: YIWEIDUILIMANCAIXIANGSHENXINBUYIDETIEGAN “FENSI”。 ZHEWEI “FENSI” MINGJIAOPENGPIAILI (Enrico Bombieri), SHIZHUMINGDEYIDALISHUXUEJIA。 LIANGRENYIGEYIXINZHONGZHONG、 YIGESHENXINBUYI, SHUIYEBUFUSHUI。 ZENMEBANNI? CHAJIERTIYIDADU。 SHUOQILAI, QISHICHAJIERDUILIMANCAIXIANGDAOYEBINGFEIQUANRANBUXIN, ERQIEYEBINGFEIYIWEIQINGSHIDUILINGDIANDESHUZHIJISUAN, TAZHISHIJUEDE 350 WANGELINGDIANSHIZAITAISHAOLE, BUZUYIRANGTAXINFU。 NEIME, YAOJISUANDUOSHAOGELINGDIANCAINENGRANGTAXINFUNI? TAKAICHUDESHUMUSHI 3 YI。 YUSHILIANGRENJIUYIZHEGESHUMUWEIXIANDINGXIALEDUYUE: RUGUOLIMANCAIXIANGZAIQIAN 3 YIGELINGDIANZHONGCHUXIANFANLI, JIUSUANCHAJIERHUOSHENG; FANZHI, RUGUOLIMANCAIXIANGBEIZHENGMING, HUOZHESUIRANMEIBEIZHENGMING, DANZAIQIAN 3 YIGELINGDIANZHONGMEIYOUCHUXIANFANLI, ZESUANPENGPIAILIHUOSHENG。 DUZHUWEILIANGPINGPUTAOJIU。

CHUKANQILAI, XIANGDUIYUYIJINGJISUANCHUDE 350 WANGELINGDIANLAISHUO, CHAJIERDE 3 YIGELINGDIANJIANZHIJIUSHI “SHIZIDAKAIKOU”, CHAJIERZIJIYEGUJIZHEGEDUJUYEXUYAOHUASHANG 30 NIANDESHIJIANCAINENGFENCHUSHENGFU。 KESHITAXIANRANGENNEIGESHIDAIDEDUOSHUQITARENYIYANG, DADADIGULEJISUANJIJISHUDEFAZHANSUDU。 SHISHISHANG, LIDUJUDESHELIHUANBUDAO 10 NIAN, 1979 NIAN, LINGDIANJISUANJIUBEITUIJINDAOLE 8,100 WANGE。 BUJIUZHIHOU, YOUBEITUIJINDAOLELIANGYIGE, JULIDUJUDEZHONGJIEZHISHENGXIALEYIBUZHIYAO, ERXINGSHIZEDUICHAJIERJIWEIBULI——YINWEINEILIANGYIGELINGDIANQUANDOUWEIYULINJIEXIANSHANG。

BUGUO, JISUANCHUNEILIANGYIGELINGDIANDESHUXUEJIADUICHAJIERDEDUJUYIWUSUOZHI, ZAIJISUANWANLIANGYIGELINGDIANHOUJIUTINGLEXIALAI, ZHEYIDIANRANGCHAJIERDADADISONGLEYIKOUQI。 KEXI, TAZHEKOUQIMEINENGSONGTAIJIU, YINWEITADEYIWEIPENGYOUQIAHAOFANGWENLENEIWEISHUXUEJIA, BUJINJIANGDUJUZHISHIGAOSULEHOUZHE, HUANJINXINGLEYIFANGUDONG。 HOUZHEYITINGLINGDIANJISUANHUANYOUZHEMEZHONGDADEYIYI, JIULIKEZHANKAILEXINDEJISUAN, YIGUZUOQITUIJINDAOLE 3 YIGELINGDIAN——DANGRAN, LIMANCAIXIANGKUIRANBUDONG。

CHAJIERSHULE, TADUIXIANNUOYANMAILAILELIANGPINGPUTAOJIU。 PENGPIAILIDANGCHANGDAKAIQIZHONGYIPINGYUTAGONGYIN。 TAMENHEDIAODEZHEPINGPUTAOJIUYONGCHAJIERDEHUASHUO, SHISHIJIESHANGBEIHEDIAODEZUIANGGUIDEPUTAOJIU, YINWEIZHENGSHIWEILEYITAWEIDUZHUDENEIGEDUJU, SHUXUEJIAMENTEYIDUOJISUANLEYIYIGELINGDIAN, WEICIHUAFEILEYUE 70 WANMEIYUANDEJISUANJINGFEI。 YEJIUSHISHUO, BEITAMENHEDIAODEZHEPINGPUTAOJIUSHIYONG 35 WANMEIYUANDEJINGFEIHUANLAIDE! HEWANLEZHEPINGPUTAOJIU, CHAJIERCONGCIYEDUILIMANCAIXIANGSHENXINBUYILE。

ZAICHAJIERHEPENGPIAILIDEDUJUZHIHOU, XIANGCHAJIERNEIYANGKANZHONGLINGDIANJISUAN、 YICIJUEDINGZIJIDUILIMANCAIXIANGXINRENDUDESHUXUEJIAYUELAIYUESHAOLE; XIANGYANZHENG 3 YIGELINGDIANNEIYANGYUANYIBAJUEJINGFEITOURUDAOLINGDIANJISUANZHONGDERENYEYUELAIYUESHAOLE。 BUGUODUILINGDIANDEJISUANBINGMEIYOUJIUCIZHONGZHI。 2001 NIAN, YIWEIMINGJIAOWEIDENIEFUSIJI (Sebastian Wedeniwski) DEDEGUOYANJIUZHECHUANGLILEYIZHONGZHANXINDEJISUANMOSHI: FENBUSHIJISUAN, JILIYONGBICILIANWANGDEXUDUOTAIJISUANJILAIGONGTONGJISUANLINGDIAN。 ZHEGEFENBUSHIJISUANXITONGJIANCHENGZHIHOU, BUJIUJIUBEITUIXIANGLEHULIANWANG, XIYINLESHIJIEGEDIDALIANGSHUXUEHEJISUANJIAIHAOZHEDECANYU, LIANWANGJISUANJIDESHUMUHENKUAIJIUWENDINGZAILE 10,000 TAIYISHANG, MEITIANJISUANCHUDELINGDIANSHUMUZAI 10 YIYISHANG。 ZHIYUJINGFEI, ZEJIBENKEYIHULVEBUJI, YINWEICANYUZHEDOUSHIZIYUANERWUCHANGDIGONGXIANCHUZIJIDEJISUANZIYUANDE。

DAOLE 2004 NIANMOSHI, WEIDENIEFUSIJIDEFENBUSHIJISUANXITONGSUOJISUANCHUDELINGDIANZONGSHUBIJINLEYIGEJIDONGRENXINDESHUMU: YIWANYI。 YANKANZHUYICIHUIHUANGQINGDIANYIZHIRIKEDAI, BULIAOQUECONGFAGUOCHUANLAILEYIGELINGRENCHIJINGDEXIAOXI: LIANGWEIFAGUORENWANCHENGLEDUI 10 WANYIGELINGDIANDEJISUAN, BITAMENQIAOSHOUQIDAIDEYIWANYIGAOCHULEZHENGZHENGYIGESHULIANGJI! GENGLINGRENCHIJINGDESHI, ZHELIANGWEIFAGUORENWANCHENGZHEYIGONGZUOSUOYONGDEJISUANZIYUANJURANZHISHIJITAIPUTONGDEJISUANJI, SUOHUAFEIDESHIJIANYEZHIYOUYINIANDUO。 CISHICIKE, ZHEYANGDEYIZEXIAOXIDUIYUWEIDENIEFUSIJILAISHUOWUYISHIDANGTOUYIBANG, JIEGUOQINGDIANBIANCHENGLEXIEMU, WEIDENIEFUSIJIZAIBUJIUZHIHOUGUANBILEZHENGGEXITONG。 CIQINGCIJING, YOURUJIUSHIDUONIANQIANYINGGUOTANXIANJIASIKETE (Robert Falcon Scott) TINGJINNANJIDEJINGLI: DANGTAMENLIJINGJIANXIN、 JIJIANGDIDANANJIDIANSHI, QUEFAXIANNUOWEITANXIANJIAAMENGSEN (Roald Amundsen) YIJINGJIEZUXIANDENG (SIKETEJITONGBANHOULAIZAIANRANFANHUIDETUZHONGQUANBUYUNAN)。

LIANGWEIFAGUORENPINGJIEJITAIPUTONGJISUANJIYINIANDUODEGONGZUO, JURANCHAOGUOLEQUANSHIJIESHANGWANTAILIANWANGJISUANJIJINIANDEGONGZUO, ERQIECHAOGUOLEZHENGZHENGYIGESHULIANGJI, ZHESHISHENMEYUANGUNI? SHIYINWEITAMENCAIYONGLEYIZHONGBILIMAN-XIGEERGONGSHIGENGGAOMINGDEJISUANFANGFA。 ZHEYIJISUANFANGFASHICHUSHENGYUBOLANDESHUXUEJIAOUDELIZIKE (Andrew Odlyzko) YUHEZUOZHEXIAOENHAGE (Arnold Sch?nhage) YU 1988 NIANSUOTICHUDE。

WU

OUDELIZIKEWEISHENMEHUIYANJIULINGDIANJISUANDESUANFANI? ZHEYEQIANCHEDAOYIDUANGUSHI, ERQIESHIHENYOUYISIDEGUSHI。 DANGRAN, BIAOMIANSHANGDEYUANYINSHIGENSUOYOUQITACONGSHILINGDIANJISUANDERENYIYANGDE, NEIJIUSHIYINWEITADUILINGDIANJISUANHENGANXINGQU。 BUGUO, TANEIXINGQUDEYOULAIGENQITARENYOUSUOBUTONG, QITARENDEXINGQUDADOULAIZIYUDUILIMANCAIXIANGBENSHENDEXINGQU, TAQUESHIYINWEITINGLEMEIGUOSHUXUEJIAMENGGEMALI (Hugh Montgomery) DEYIGEBINGFEIZHIJIEZHENDUILIMANCAIXIANGDEYANJIUBAOGAO, CAICONGSHILINGDIANJISUAN, BINGYANJIULINGDIANJISUANDESUANFADE。 MENGGEMALINEIGEBAOGAOSUOJIESHAODESHIYIXIANGHENDUTEDEYANJIU, JIYANJIULIMAN ζ HANSHUFEIPINGFANLINGDIANZAILINJIEXIANSHANGDEFENBUGUILV。 TADEYANJIUBIAOMING, ZAISHIDANGDEJIASHE——QIZHONGBAOKUOJIASHELIMANCAIXIANGCHENGLI——XIA, KEYIZHENGMINGLIMAN ζ HANSHUDEFEIPINGFANLINGDIANZAILINJIEXIANSHANGDEFENBUCHENGXIANCHUYIZHONGXIANGHUPAICHIDEQUSHI (JIQINGXIANGYUBICIYUANLI), ZHEGEQUSHIKEYIYONGYIGEBUTAIFUZADESHUXUEGONGSHILAIMIAOSHU。

MENGGEMALIZI 20 SHIJI 70 NIANDAICHUJIUKAISHIYANJIULIMAN ζ HANSHUFEIPINGFANLINGDIANZAILINJIEXIANSHANGDEFENBUGUILVLE。 TAFAXIANLEGUILV, BINGQIEYINWEINEIGUILVBUTAIFUZAERZHIJUEDIGANDAOZAIQIBEIHOUYINGGAIYUNHANZHUMOUZHONGXUANJI。 WEILEJIEKAINEIXUANJI, TATEYIFANGWENLEPULINSIDUNGAODENGYANJIUYUAN。 ZAINEILI, TA “JINJIAN” LELIMANCAIXIANGYANJIUDEYUANLAOSAIERBOGE。 KEXIJIULIANSAIERBOGEYEKANBUTOUNEIGUILVBEIHOUDEXUANJI。 BUGUO, ZAIGAODENGYANJIUYUANNEIYANGYIGEMINGJIAYUNJIDEDIFANG, SUISHIDOUYOUKENENGCHUXIANYIXIANGBUDAODEXUESHUJIAOLIU。 MENGGEMALIZAIZUIYOUXIWANGDEDAOXINXIDESAIERBOGENEILIBUCENGDEDAOYOUJIAZHIDEXINXI, QUEZAIGAODENGYANJIUYUANDECHASHILIOUYULEYIWEIWULIXUEJIA。 NEIWEIWULIXUEJIAMINGJIAODAISEN (Freeman Dyson), SHIYIWEIYANJIULINGYUHENKUANGUANGDERENWU, DANGTAZAIHEMENGGEMALIDEPANTANZHONGHUOZHIHOUZHESUOFAXIANDEZHEGELINGDIANZAILINJIEXIANSHANGDEFENBUGUILVSHI, DENGSHIJIUCHILEYIJING。 YINWEITAXIANGQILEZIJISHIDUONIANQIANDEYIXILIEYANJIU。 NEIXIEYANJIUGENLIMAN ζ HANSHUDEFEIPINGFANLINGDIANMEIYOUBANDIANGUANXI, DANZAINEIXIEYANJIUZHONG, TAQUEDEDAOGUOTONGYANGDEFENBUGUILV!

DAISENSHIDUONIANQIANSUOYANJIUDESHISHENMENI? SHICONGYIXIEJIWEIFUZADEWULITIXI——BIRUFUZAYUANZIHE——ZHONGCHOUXIANGCHULAIDEWENTI。 CHULINEIZHONGWENTISUOYONGDESHIYILEITESHUDETONGJIWULISHOUDUAN, ERQIZHONGYIGEDIANXINGDEKETIZESHIYANJIUFUZATIXIZHONGNENGLIANGDEFENBU——WULIXUEJIAMENCHENGZHIWEINENGJIFENBU。 DAISENCENGJINGDEDAOGUONEIZHONGFENBUDEJUTIXINGSHI, TACHULEKEYIMIAOSHUNENGJIWAI, HUANCHUXIANZAILEXUDUOQITAFUZADEWULIXIANXIANGZHONG。 ERXIANZAI, CONGMENGGEMALISUOCONGSHIDECHUNSHUXUEYANJIUZHONG, TAJURANZAICIJIANDAOLETONGYANGDEFENBU, ZHESHIZAISHIDADACHUHUTAYILIAODESHIQING。

JINIANZHIHOU, MENGGEMALIZAICILAIDAOPULINSIDUN, BINGZUOLEYICIYANJIUBAOGAO——JIOUDELIZIKESUOTINGDAODEBAOGAO。 ZAIBAOGAOZHONG, TACHULEJIESHAOZIJIDEYANJIUWAI, HUANTIDAOLETAHEDAISENSUOFAXIANDEZHEZHONGSHUXUEYUWULIZHIJIANDEQIGUAILIANXI。 ZHEYIQIEYINQILEOUDELIZIKEDENONGHOUXINGQU, SHITAJUEDINGTONGGUODAGUIMOLINGDIANJISUANLAIYANZHENGMENGGEMALISUOFAXIANDELINGDIANZAILINJIEXIANSHANGDEFENBUGUILV。 CONG 20 SHIJI 80 NIANDAIMODAO 90 NIANDAICHU, OUDELIZIKELIYONGTAHEHEZUOZHEXIAOENHAGESUOTICHUDEXINSUANFA, WANCHENGLEJIPIDAGUIMODELINGDIANJISUAN, JIEGUOFEICHANGPIAOLIANGDEZHENGSHILEMENGGEMALISUOTICHUDELINGDIANZAILINJIEXIANSHANGDEFENBUGUILV。 KAOLVDAOMENGGEMALIDEJIEGUOSHIZAIJIASHELIMANCAIXIANGCHENGLIDEJICHUSHANGDEDAODE, YINCIZHEZHONGZHENGSHIYEKEYIZAIYIDINGCHENGDUSHANGBEISHIWEISHIDUILIMANCAIXIANGDEJIANJIEZHICHI。

BUGUO, SUOYOUZHEXIEDOUMEIYOUJIEJUEYIGEZUIGENBENDEWENTI, NEIJIUSHIXIANGLIMAN ζ HANSHUFEIPINGFANLINGDIANZAILINJIEXIANSHANGDEFENBUZHEYANGZUICHUNCUIDESHUXUEXINGZHI, WEISHENMEHUIGENXIANGFUZAYUANZIHEDENENGJIFENBUNEIYANGZUIXIANSHIDEWULIXIANXIANGCHESHANGGUANXI? ZHEZHONGSHENQIDEGUANLIANBENSHENYOUYUSHIZHUSHENMENI? ZHELIANGGEWENTIZHIDAOJINTIANYEMEIYOUWANQUANDEDAAN。 DANYOUYISIDESHI, ZAIBANGEDUOSHIJIQIAN, QUEYOULIANGWEISHUXUEJIACENGJINGTICHUGUOYIGECAIXIANG——YIGEYUMENGGEMALI、 DAISEN、 OUDELIZIKESUOFAXIANBINGZHENGSHIDEZHEZHONGSHUXUEYUWULIJIANJINHULIQIDELIANXIYAOXIANGHUYINGDECAIXIANG。 NEILIANGWEISHUXUEJIADEMINGZIWOMENZAIQIANWENZHONGCENGJINGTIDAOGUO, YIWEISHIXIERBOTE, YIWEISHIBOLIYA, NEIGECAIXIANGZEBEICHENGWEIXIERBOTE-BOLIYACAIXIANG, TASHIDUILIMAN ζ HANSHUFEIPINGFANLINGDIANFENBUDECAICE, QIZHONGHERANBAOKUOLECAICETAMENYUMOUGEWULITIXIDENENGJIXIANGDUIYINGDEKENENGXING!

BUGUOZHEGEXIERBOTE-BOLIYACAIXIANGBENSHENYEPOYOUYIXIELIQIDEDIFANG, YINWEIDANGRENMENYINMENGGEMALI、 DAISEN、 OUDELIZIKEDEYANJIUERDUITAFASHENGXINGQU, SHITUZHUISUTADEQIYUANSHI, QUEJINGYADIFAXIANWULUNXIERBOTEHUANSHIBOLIYA, JURANDOUBUCENGZAIRENHEWENZIZHIZHONGSHUJIGUOZHEGECAIXIANG。 NANDAOZHEGECAIXIANGGENBENJIUSHIZIXUWUYOUDECHUANSHUO? XINGYUNDESHI, 94 SUIGAOLINGDEDANGSHIRENBOLIYANEISHIRENGJIANZAI, TAZAIYIFENGXINJIANZHONGYIGERENHUIYIDEFANGSHIKENDINGLEZHEYICAIXIANGDECUNZAIXING。 DANZAOYIQUSHIDEXIERBOTEZAISHENMECHANGHEXIATICHUGUOZHEYICAIXIANG, QUEHENKENENGJIANGCHENGWEISHUXUESHISHANGYIGEYONGJIUDEMITUANLE。

LIU

JIESHAOLEZHEXUDUOYOUGUANLIMANCAIXIANGDEYANJIU, YOUYIGEWENTIXIANGBIHENDUODUZHEDOUHUIGUANXIN, NEIJIUSHILIMANCAIXIANGDEZHONGJIMINGYUNJIANGHUIRUHE? TASHIHUIBEIZHENGMINGNI? HUANSHIHUIBEITUIFAN (FOUZHENG)? DUIYUZHEGEYOUGUANLIMANCAIXIANG “QIANTUMINGYUN” DEDAXUANNIAN, SHUXUEJIAMENGEYOUGEDEKANFA。

YOUXIESHUXUEJIAXIANGXINLIMANCAIXIANGSHIDUIDE, BIRUNEIWEISHUDIAOLEPUTAOJIUDECHAJIERZIDUJUGAOFUZHIHOUJIUDUILIMANCAIXIANGSHENXINBUYI。 TAXIANGXINLIMANCAIXIANGDELIYOUHEN “CHUNPU”, NEIJIUSHISHUZHIZHENGJUYIJINGGOUQIANGLE。 DUZHEMENXIANGBIHUANJIDE, TADANGSHIYAOQIUDESHUZHIZHENGJUSHI 3 YIGELINGDIAN, XIANZAIDEZHENGJUYIJINGCHAOGUOLE 10 WANYI, YUANYUANCHAOCHULETADEYAOQIU。 YINCI, TADEXIANGXINSHIYOULIYOUDE。 BUGUO, YOUYULINGDIANYOUWUQIONGDUOGE, SHIJISHANGZAIDUODESHUZHIZHENGJUYESHIWEIBUZUDAODE。 ERQIEZAISHUXUESHANGYOUGUOZHEYANGDELIZI, JIYIGEBEIFOUZHENGLEDESHUXUEMINGTIDESHUZHIFANLICHUXIANZAIJIYAOYUANDEDIFANG, YUANYUANCHAOCHUSHUZHIZHENGJUSUONENGCHUJIDEFANWEI。 LIMANCAIXIANGHUIBUHUIYESHIRUCINI? SHUIYESHUOBUZHUN。 DANGRAN, ZHICHILIMANCAIXIANGDEZHENGJUBUJINJINLAIZISHUZHIJISUAN, HUANYOUWOMENJIESHAOGUODEDALIANGQITAYANJIU, QIZHONGBAOKUOZHISHAOYOU 40% DEFEIPINGFANLINGDIANWEIYULINJIEXIANSHANGNEIYANGPOWEIKEGUANDEJIEGUO。 XIANGXINLIMANCAIXIANGDESHUXUEJIAMENYEKEYICONGNEIXIEFANGMIANHUODEXINXIN。

YOUXIESHUXUEJIAZERENWEILIMANCAIXIANGSHICUODE。 MIANDUILIMANCAIXIANGSUODEDAODERUCIHAILIANGDEZHICHI, XUANZENEIYANGDELICHANGDANGRANSHIYAOLIYOUDE。 ZHEQIZHONGYITIAODABUDAODELIYOUJIUSHI: SUOYOUZHICHIDOUBUSHIZHENGMING。 QUESHI, DUIYUXIANGLIMANCAIXIANGZHEYANGDESHUXUEMINGTILAISHUO, YAOXIANGZHENGMINGTACHENGLI, BIXU “YIGEDOUBUNENGSHAO” DIHANGAISUOYOUDELINGDIAN, QUEYIDINGDIANERDOUBUXING。 DANFANGUOLAI, YAOXIANGTUIFANTA, QUEZHIYAOZHAODAOYIGEFANLI——JIYIGEBUZAILINJIEXIANSHANGDEFEIPINGFANLINGDIAN——JIUZUGOULE, ZHEZHONGFANJIANCHENGDUSHANGDEBUDUICHENGDUIYUHUAIYILIMANCAIXIANGDESHUXUEJIAMENSHISHIFENYOULIDE。

CHUSHANGSHULIANGZHONGJIERANXIANGDUIDETAIDUWAI, LIMANCAIXIANGDECHANGQIXUANERWEIJUEHUANSHIYIXIERENLIANXIANGDAOLESUOWEIDEGEDEERBUWANQUANXINGDINGLI (G?del"s incompleteness theorem), RENWEILIMANCAIXIANGYOUKENENGSHIYIGEBUNENGBEIPANDING——JIJIBUNENGBEIZHENGMING, YEBUNENGBEIFOUZHENG——DEMINGTI。 JUSHUOGEDEER (Kurt G?del) BENRENJIUYOUGUOZHEYANGDEKANFA。 BUGUO, LIMANCAIXIANGJIARUBUCHENGLI, ZAIYUANZESHANGSHIKEYIYONGMINGQUEDEBUZOU, TONGGUOSHUZHIJISUANZHAODAOTADEFANLI, CONGERZHENGMINGQIBUCHENGLIDE。 CONGZHEGEYIYISHANGJIANG, LIMANCAIXIANGJIARUBUCHENGLI, TASHIKEYIBEIPANDINGWEIBUCHENGLIDE, ERTARUGUOBUNENGBEIPANDING, SHIJISHANGSHIBIAOMINGTACHENGLI。

HAOLE, YISHANGJIUSHIDUILIMANCAIXIANGDEJIANDANJIESHAO。 ZHEYIJIESHAOYINWEILVEQULESHUXUEXIJIEERKANSHANGQUGENGXIANGSHIYICHUANGUSHI。 DANSHIJISHANG, LIMANCAIXIANGSHIYIGEJIWEIJIANSHENDEKETI, RUGUONAWEIDUZHEXIANGYAOKENYIKENZHEGECAIXIANG, SHOUXIANYAOYOUZHASHIDESHUXUEGONGDI, FOUZEFEIDANKENBUDONG, HUANHENKENENGHUIBENGDIAOYACHI——KEBIEGUAIWOMEITIXINGE。

ERLINGYIERNIANSANYUESIRIXIEYUNIUYUE

ERLINGYIERNIANSANYUESHILIURIFABIAOYUBENZHAN