佩雷尔曼的非凡人生与成就
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原文标题：数学鬼才佩雷尔曼
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文章类别：新闻报道
《少年游·涅瓦寒窗》（成长经历）
霜风凛冽夜微沉，孤影对寒灯。 拓扑无边，几何浩渺，静掘数层深。
涅瓦静水浮冰冷，冷眼望浮云。 命运如题，难求一解，独自问前程。
《水调歌头·百年困锁》（攻克难题）
千载谜踪暗，百年梦难成。 庞门一锁横设，几度困群英。 变换虚空回转，曲面交缠无尽，影碎数层冰。 拓扑回环里，真理待谁听？
寒灯下，霜夜久，算无声。 孤影沉思不语，几度理纷纭。 笔落三维拓境，算破千重幻影，万象忽分明。 窗外街灯冷，夜静映书屏。
《雨霖铃·尘世微声》（成名后的纠纷与归隐）
疑云渐散，世间风起，喧嚣如浪。 旧案沉封百载，骤然惊破，纷言相向。 谁借微光添己色，妄意攀名状。 他却自沉寂，冷眼千峰孤望。
长夜无声尘影忘。 看万语翻腾，终散虚网。 两拒金章，回首人间皆过往。 空余旧帖余叹在，寥落无人响。 时序入流转，微雨街灯晃。
数学鬼才佩雷尔曼
├── 颁奖事件引言
│ ├── 佩雷尔曼缺席千禧数学奖颁奖
│ └── 之前拒绝菲尔兹奖
├── 类比引入佩雷尔曼的成就
│ ├── 地理发现的类比
│ └── 佩雷尔曼证明庞加莱猜想
├── 数学家们的评价和反应
│ ├── 阿蒂亚的赞扬和表示不认识佩雷尔曼
│ ├── 瑟斯顿的钦佩和表示未见过佩雷尔曼
│ └── 格罗莫夫的推测和介绍
├── 1 小佩雷尔曼的成长环境
│ ├── 家庭背景和反犹太主义环境
│ ├── 母亲的教育方式
│ ├── 数学思维方式的形成
│ ├── 数学俱乐部老师鲁克辛的影响
│ └── 专业数学学校的学习
├── 2 佩雷尔曼的学术生涯早期
│ ├── 参加几何节和在美国的博士后工作
│ ├── 独特的生活方式
│ └── 与田刚的交往
├── 3 佩雷尔曼的学术突破与“消失”
│ ├── 解决“灵魂猜想”
│ ├── 遭遇研究瓶颈
│ └── 突然发布庞加莱猜想的证明
├── 4 佩雷尔曼的“复出”与隐退
│ ├── 发送邮件给数学家们
│ ├── 在美国大学巡回讲座
│ ├── 媒体报道和与田刚的“误会”
│ ├── 与外界的隔绝和媒体的关注
│ └── 与《纽约客》作者的会面
├── 5 数学界的争议与佩雷尔曼的态度
│ ├── 汉密尔顿的反应
│ ├── 曹怀东和朱熹平的论文争议
│ ├── 拒绝菲尔兹奖和千禧数学奖
│ └── 对生活的态度和反思
└── 结语
└── 参考书目致谢
文章标签：
#数学家 #佩雷尔曼 #庞加莱猜想 #千禧数学奖
（原文）
即便是在“怪人”云集的数学家群体中，佩雷尔曼也是一个特殊的怪人。6 月 8 日，世界上一批最优秀的数学家聚集在巴黎，给俄罗斯数学家佩雷尔曼颁发千禧数学奖，但是他却不在场。此前他还拒绝了数学界的最高荣誉——菲尔兹奖。
他再次放弃了为他人可望不可即的荣誉，同时也放弃了一百万美元的奖金。
假设你完全不知道地球的地理情况，你一次又一次派出远征的船队，这些船队接连发现新的大陆。直到已知大陆的数量增长到六块。可是你并不知道这是否就是地球上所有的大陆了。你继续派出船队，前前后后出征了几百次，但是他们没有再发现任何新的大陆。这时你提出一个猜想：地球上没有更多的大陆了。
这个猜想看起来很合理，但是它仍需要论证。这时，佩雷尔曼出现了，他用完美的严密方式向你和全世界证明，地球上确实没有更多的大陆了。
以上是俄罗斯数学家米哈伊尔·格罗莫夫（Mikhail Gromov）的一个比方。现实中的格里戈里·佩雷尔曼（Grigoriy Perelman）并不是一名地理学家，而是一名数学家。他在数学上所做出的工作的重要性完全不亚于上面的这个比方——他建造了一套漂亮的证明来确认“庞加莱猜想”的正确性。
6 月 8 日，世界上一批最优秀的数学家聚集在巴黎海洋学研究所，那里离亨利·庞加莱研究所很近。“亨利·庞加莱去世一个世纪之后，在他生活和工作过的这座城市里，他遗赠给我们的猜想被解决了。格里戈里·佩雷尔曼是登顶那个三维世界的登山者。”英国爱丁堡大学数学家迈克尔·阿蒂亚（Michael Atiyah）在赞颂佩雷尔曼的发言中说。
81 岁高龄的阿蒂亚是 20 世纪最具影响力的数学家之一，他在 1966 年就获得数学界的最高奖菲尔兹奖。然而，他对南方周末记者说：“我不认识佩雷尔曼。”
美国康奈尔大学数学家威廉·瑟斯顿（Wiliam Thurston）早在 1970 年代就提出了一个几何化猜想，他在 1980 年的一次会议上大胆表示，他的这个几何化猜想把庞加莱猜想放在了一个更加完整的框架之中。他对几何化猜想相当乐观，认为它一定能够得到证明，但他并不知道这是否会发生在他的有生之年。他自己投入了大量的精力来证明这个猜想，却始终没有成功。
“佩雷尔曼，带着极大的兴趣和精湛的技艺，在我和其他人失败之处建立了一个漂亮的证明。”瑟斯顿说，“这是一个我无法做到的证明：佩雷尔曼的某些强项正是我的弱点。”
“我很荣幸能有这样一个机会来公开表达我对格里戈里·佩雷尔曼的深深钦佩和欣赏。”瑟斯顿在发言时说。然而，他也告诉南方周末记者：“我没有见过佩雷尔曼，我也未能出席他以前的讲座。”
十余名世界级的数学家在巴黎为佩雷尔曼颁发千禧数学奖，他们中的多数人却从未与佩雷尔曼谋面，或是有任何接触。更重要的是，佩雷尔曼本人没有到场。
这不但意味着佩雷尔曼忽视了一个其他人可望不可即的荣誉，也意味着他放弃了一百万美元的奖金。
“佩雷尔曼可能有很多理由来拒绝这个奖项，但我不想揣测。”格罗莫夫对南方周末记者说，“事实上，只有一个理由让他领奖——钱，但有很多的理由让他拒绝。”
格罗莫夫是世界上少有的几位与佩雷尔曼有过接触的数学家。实际上，是他让国际数学界认识了那名特立独行的数学天才。
2003 年 4 月，佩雷尔曼来到美国麻省理工学院，开始他在美国大学中的巡回讲座。
小佩雷尔曼生活在一个母亲帮助下建立起来的想象世界中，除了数学，几乎没有其他东西。
佩雷尔曼 1966 年出生于苏联的一个犹太人家庭，他的母亲是大学里的数学教师。这似乎为他数学天分的发展提供了一个有利条件，但苏联社会中广泛存在反犹太主义也为佩雷尔曼的成长与生活构造了残酷的环境。
如何向孩子讲述生活的残酷，是常常会令家长头疼的问题。佩雷尔曼的母亲选择了一种特别的方式——她把自己头脑中的正确世界当作真实的世界告诉年幼的佩雷尔曼。
所以，在佩雷尔曼的世界里，反犹太主义是不存在的。这样的世界至少持续到了他的大学阶段。在任何普通人看来都再明显不过的反犹太主义却在佩雷尔曼那里不成立，这与佩雷尔曼数学式的思维方式有很大关系。举一个例子来说，列宁格勒大学每年只招收两名犹太学生，这很容易被认为是种族歧视的典型表现。但是在佩雷尔曼入学那年，由于佩雷尔曼在国际数学奥林匹克竞赛上拿了奖牌，他被获准面试入学，那么与另外两名考进来的犹太学生一起，这一年列宁格勒大学就招收了三名犹太学生。如果说每年只招收两名犹太学生是反犹太主义存在的证明的话，那么也许在佩雷尔曼看来，这一年招收了三名学生就是这一命题的反例。
社会生活中模糊的变数是佩雷尔曼所难以理解的，这一点在他年幼时就已经形成。他的数学俱乐部老师鲁克辛（Sergey Rukshin）每周会有两个晚上与佩雷尔曼同路乘火车回家。冬天的时候，佩雷尔曼会戴着一顶苏联样式的皮帽子，帽子在耳朵的部位有两块皮子，用绳子系紧之后能够防止耳朵受冻。鲁克辛发现，即便在温暖的车厢里，佩雷尔曼也从不解开绳子。“他不仅是不会摘掉帽子，”鲁克辛在一本书中说，“他甚至不会解开帽子的耳朵，他说不然的话妈妈会杀了他，因为妈妈说了，不要解开绳子，不然就会感冒。”
鲁克辛曾经批评佩雷尔曼读书不够多，他认为他的职责不单是教孩子们数学，还要包括文学和音乐。佩雷尔曼就问鲁克辛，为什么要读那些文学书。鲁克辛告诉他，因为这些书是“有趣的”，而佩雷尔曼的回答是，需要读的书应该都列在学校的必读书单上了。
也是由于看到佩雷尔曼这样的个性，鲁克辛作为一名数学竞赛的教练，从来不用担心佩雷尔曼在数学训练中会存在“分心”的状况。佩雷尔曼确实从不分心。他的同班男孩们长大一些后开始与女孩子接吻，鲁克辛就常常去抓他们。但佩雷尔曼从不对女孩子感兴趣。
佩雷尔曼生活在一个母亲帮助下建立起来的想象世界中，这个世界里规矩就是规矩，而且除了数学，几乎没有其他东西。鲁克辛是对儿童时期的佩雷尔曼影响最大的数学教练，佩雷尔曼也成了鲁克辛生命的一部分。他让佩雷尔曼在列宁格勒的生活安全、有序，就像佩雷尔曼想象中的世界一样，一直把他送进 239 号专业数学学校。
列宁格勒的 239 号专业数学学校是数学家安德雷·柯尔莫格洛夫（Andrei Kolmogorov）创办的一所学校，这里的数学教育与普通高中里的不同，它一方面教授现实研究当中的数学，一方面也根据不同学生的背景施教。它也是苏联高中里惟一教授古代历史课程的学校。学生在这里还会接触到音乐、诗歌、视觉艺术、古俄国建筑的知识。但这里并没有苏联学校里普遍开设的其他社会科学课。
在老师和学校为他创造的微环境当中，佩雷尔曼与真实的世界始终保持隔绝，他自己的世界也就得到了保护和延续。与其他数学专长的年轻人坐在一起上课的时候，佩雷尔曼总是坐在后排。他一语不发，只有当发现某个人的解法或解释需要订正时才说话，而且总是一锤定音。也许很多时候，课堂上讲授的内容对佩雷尔曼毫无用处，但他也会静静地听着，他从来就是一个礼貌的人，因为规矩就是规矩。
佩雷尔曼的另一条行事原则是，必须讲出完整的事实，不然的话，他便可能认为那是政治。在参加全苏联数学竞赛的时候，每个学生会被发给一道题目，谁解出来了便对老师举手示意，然后老师把他带到教室外面。他把解法讲给老师，如果正确，老师就会发给他下一道题，如果错误，就继续回去做这道题。最终的胜负是看谁在规定时间内解出的题目最多。有一次，佩雷尔曼解出了题目，老师把他叫到外面，他向老师解释一番之后，老师说了句“正确”便要转身回教室。可佩雷尔曼却把老师叫住，他说，这道题还有另外三种可能的结果！他坚持要把所有的可能性告诉老师，即便这样做对于数学竞赛来说等于是浪费时间。
到了中学的最后一年时，佩雷尔曼已经在全苏联数学奥林匹克竞赛中赢得了 一块金牌和一块银牌，并最终在 1982 年的国际数学奥林匹克竞赛中以 42 分的满分拿到了金牌。
对“灵魂猜想”的证明，使得佩雷尔曼成为数学界年轻的明星。让所有人惊讶不已的是，他只用了四页纸。
1991 年，格罗莫夫帮助佩雷尔曼到美国东海岸参加了几何节。在此之前，佩雷尔曼在列宁格勒大学读了六年书，也是在此期间，他选择了朝向几何学的方向发展。
几何节是个一年一度的数学会议，那一年在杜克大学召开。佩雷尔曼是几何节上七名报告人之一，他做了题为“曲率有下界的 Alexandrov 空间”的报告。这个题目的论文在一年后发表，成为他的代表作之一。
在几何节期间，格罗莫夫向各个重要的人士介绍了佩雷尔曼，使得这次旅行让佩雷尔曼获得了到美国做博士后工作的机会。
杰夫·齐杰（Jef Cheeger）是美国纽约大学库朗（Courant）数学研究所的数学家，他在这一届的几何节上也有报告。他注意到了佩雷尔曼。他在格罗莫夫的介绍之下与佩雷尔曼会面。一年之后，也就是 1992 年的秋天，佩雷尔曼来到库朗研究所，开始了他的博士后时光。
即便是在“怪人”云集的数学家群体中，佩雷尔曼也是一个特殊的怪人。他似乎永远都穿同一件衣服，胡子拉碴，不剪指甲——他认为这样才是指甲的自然状态。他的食物只有面包和酸奶。美国的面包对他来说可能并不好吃，好在他找到了一家售卖正宗俄罗斯面包的商店，经常步行一段距离到那里买面包。所以，他没有什么地方需要开销，他把所有的津贴都留在银行里（这为他存了一笔钱，保证后来的一段时间里他能在俄罗斯温饱无忧）。
佩雷尔曼一辈子都没有离开过他的母亲。在纽约做博士后期间，他的母亲随他来到美国，住在布鲁克林，照顾佩雷尔曼的日常生活。
我们不知道佩雷尔曼在他的一生中有过多少个朋友，但可以肯定的是，数量非常少。在纽约大学期间，他难得地交到了一个朋友。佩雷尔曼的老师维克托·查加勒（Viktor Zalgaler）非常肯定这一点。他的这位朋友就是田刚，现在的普林斯顿大学和北京大学数学教授。
那个时候，佩雷尔曼经常与田刚交谈。不过在田刚的记忆中，他们的谈话都是关于数学本身的，没有涉及过其他事情。他认为佩雷尔曼也许会跟其他某个友善的人聊一聊其他话题，但并不是他。田刚知道佩雷尔曼会去布鲁克林桥附近买面包，但由于田刚本人并不在乎吃这种面包或是那种，所以他也并不清楚佩雷尔曼喜爱的面包究竟有何特别。
1993 年，佩雷尔曼解决了数学上一个长期存在的问题——“灵魂猜想”（Soul Conjecture）。这是一个由齐杰和另一名数学家提出来的猜想。在二十年的时间里，已经有一些人写了长篇大论来分析这个问题，但仅仅只能做出部分的证明。佩雷尔曼则做了一个能够让所有人惊讶不已的完整证明——而且，他只用了四页纸！
对“灵魂猜想”的证明，使得佩雷尔曼成为数学界的年轻明星。这一年，他才 27 岁。他在同一年的秋天搬去了美国西海岸的加州大学继续他的研究工作。但是，佩雷尔曼开始遭遇数学上的失败，这很可能是他人生中的第一次失败。他在 Alexandrov 空间的研究上卡壳了，停滞不前。1994 年很可能是令他充满了挫败感的一年。后来，就没有人知道他究竟在研究什么了，直到八年之后他突然在互联网上张贴出庞加莱猜想的证明。
在 1990 年代解决了一系列著名问题后，他就消失了。现在他又浮出了水面。
2002 年 11 月 12 日，美国纽约州立大学数学家迈克尔·安德森（Michael Anderson）突然收到了一封来自佩雷尔曼的电子邮件。此时佩雷尔曼已经回国多年。信中，佩雷尔曼只说了一句话：“我想请你留意我在 ArXiv 张贴的论文 arxiv.org/abs/math/0211159 ”然后就是论文摘要部分的复制。
安德森是十来名收到相同邮件的数学家之一，这些数学家都是多年来从不同侧面研究庞加莱猜想的人士。安德森在收到邮件的第二天凌晨 5 点 38 分又给其他一些数学家发了邮件（看起来他很可能彻夜阅读了佩雷尔曼的论文），希望他们能帮忙看看这篇论文的可靠性究竟有多大。“在我看来论文中的想法是全新的和原创的——典型的格里沙（佩雷尔曼的昵称）风格。”安德森在邮件中写道。他还说：“他在 1990 年代解决了一系列其他领域中著名的问题，然后就‘消失’ 了。现在看来他又浮出了水面。”
ArXiv 是美国康奈尔大学图书馆办的一个网站，供数理科学家张贴论文预印本。佩雷尔曼张贴的这篇论文是他证明庞加莱猜想的三篇文章的第一篇。第二篇和第三篇论文在 2003 年张贴。整个过程如同行云流水，然而，他的同行们需要用一两年的时间才能理解这三篇文章。
2003 年 4 月，佩雷尔曼来到美国麻省理工学院，开始他在美国大学中的巡回讲座。即便是他这样沉静、内向、低调的数学家，也按捺不住急切地与人分享的心情，每天都在研讨会上向不同的听众讲解他的证明。佩雷尔曼非常有耐心地一点点讲解，并乐于回答听众提出的每一个问题。当然，这种分享仅限于数学圈之内，他只想讲给那些有可能理解他的工作的人听。
然而，《纽约时报》的记者捕捉到了这个信息，在报纸上发表了一篇报道，题目是“俄罗斯人宣称解决了一个著名的数学问题”。这篇报道很可能令佩雷尔曼不快。首先，他并没有“宣称”什么，他只是在与同行们讨论。更重要的是，报道当中提到，如果佩雷尔曼的证明经受住了同行两年的考察，那么他可能会获得一百万美元的奖金，也就是克雷研究所的千禧数学奖。这样的写法给人一种错误印象：佩雷尔曼似乎是冲着奖金来的。但实际上，佩雷尔曼早在克雷研究所设立百万美元大奖之前就已经投入证明庞加莱猜想的工作中了。
在这个时候，佩雷尔曼的朋友田刚也犯了一个“错误”。2004 年春，田刚接受了美国《科学》杂志的采访，谈及佩雷尔曼的工作。随后，他就发现佩雷尔曼不再回复他的电子邮件了。
实际上，佩雷尔曼的论文也是田刚研究工作的重要方向，他和另一名拓扑学家约翰·摩根（John Morgan）组成的团队是世界上三个核实佩雷尔曼证明的团队之一。
“2002 到 2006 年间，除了他在麻省理工的时间，我们在数学方面有一些联系。他在访问麻省理工期间，我们聊了很多，大部分是关于数学的。”田刚回忆，“他回到俄罗斯之后的许多年里，我们几乎没有联系。”
没有人确切地知道佩雷尔曼为什么不再理睬他的老朋友了，但他看起来做得 很彻底。摩根和田刚将他们的研究结果写成了书，并且用邮寄的方式送给佩雷尔曼。但过了一阵子，邮件被退回到他们手中。
田刚这样向南方周末记者讲述这件事情：“在成书之后，我们确实寄送给了可能会对此感兴趣的几个人，其中包括佩雷尔曼。鉴于他的工作是直接相关的，我们送了他一本，看他能否做出评论。这是一种标准做法。但是手稿被退回了，说地址错误。我们没有想太多。也许我们没把地址写对。”
他切断了与外界的所有联系。与此同时，外部世界则对他充满了好奇，无数的媒体开始围在他家周围。
如果说这个世界上有任何人在评价佩雷尔曼的工作上具有权威，那么他应该是美国哥伦比亚大学数学教授理查德·汉密尔顿（Richard Hamilton）。汉密尔顿在数学上最著名的贡献就是发现了 Ricci 流，而 Ricci 流正是让佩雷尔曼接近顶峰的助手。
佩雷尔曼发表论文之前的许多年里，汉密尔顿自己以及围绕他形成的所谓“Ricci 流共同体”也一直试图证明庞加莱猜想，但从未遂愿。这段时光里，汉密尔顿是否知道佩雷尔曼都是一个疑问。佩雷尔曼曾经去听过汉密尔顿的讲座，他实际上是对汉密尔顿心怀敬意的，他还在讲座之后向汉密尔顿请教过问题。那个时候的汉密尔顿显得亲切友善。
然而，当佩雷尔曼这个“Ricci 流共同体”之外的陌生人带着他的答案来到美国四处讲座的时候，汉密尔顿保持了沉默。作为一个最该出现的人，他并没有很快在讲座上出现。只有当佩雷尔曼的巡回讲座抵达哥伦比亚大学去的时候，汉密尔顿才终于出现在教室里。听完了佩雷尔曼的讲解，他简单地问了几个问题；在佩雷尔曼看来，这些问题毫无深度，也许他连他的论文都没有读完。
2004 年 5 月，佩雷尔曼回到了圣彼得堡，他与少年时代的数学老师鲁克辛一起散步，他告诉老师，他对数学界感到失望。2005 年 12 月，在没有明确原因的情况下，佩雷尔曼辞去了莫斯科 Steklov 数学研究院的职务。
由此，佩雷尔曼再一次从世界上“消失”了。佩雷尔曼切断了与外界的所有联系，他平时只与自己的母亲和老师鲁克辛交谈。与此同时，外部世界则对佩雷尔曼充满了好奇，自从俄罗斯的这位世界级数学明星诞生以来，俄罗斯无数的媒体开始围在他家周围。
“只要我不是惹人注意的，我就有得选择。”佩雷尔曼有一次说道，“或者去做某种丑陋的事情，或者，如果我不做这种事，我就被像宠物一样对待。现在，我成了引人注意的人，我不能再做保持沉默的宠物。这就是我为什么要退出。”
佩雷尔曼不仅仅是辞了工作，他实际上是退出了数学界。
在所有的外人当中，《纽约客》的两名作者是幸运的，他们成了这个世界上仅有的与佩雷尔曼本人聊了数个小时的记者。
2006 年 6 月，他们飞往圣彼得堡。在此之前，他们向佩雷尔曼的电子邮箱里发了几封信，希望他能够安排见面。基本上毫无悬念地，他们没有收到任何回复。到达圣彼得堡后，他们乘出租车来到佩雷尔曼居住的公寓。
他们没有敲门，而是在佩雷尔曼的信箱里放了一本书——约翰·纳什的文集，并留了张字条，告诉佩雷尔曼，他们转天下午会在附近操场的一条长椅上等他。第二天，两名作者在长椅上等了一下午，佩雷尔曼没有出现。
于是，两人又在佩雷尔曼的信箱里留了一盒珍珠奶茶和另一张字条，列举了想要跟他讨论的问题。佩雷尔曼仍然没有回应。两人就又重复了一次。佩雷尔曼还是没有回应。
于是两人以为佩雷尔曼并不在家。于是他们按了门铃，希望至少能与佩雷尔曼的母亲谈一谈。一名妇女开了门，把他们让进屋去。佩雷尔曼就在屋里。与佩雷尔曼打了招呼之后，两名作者才知道，他已经数月没有查过电子邮件，整整一周没有开过自家信箱了，所以他根本不知道眼前的两人是谁。
第二天，佩雷尔曼与这两名不速之客在圣彼得堡的大街上逛了四个小时，然后又一起观看了五个小时的声乐比赛。他反复告诉他们，他已经不在数学界了，并且不认为自己是一名专业数学家了。他还对他们说：“我想交一些朋友，他们不必是数学家。”
两名作者回到美国后在《纽约客》上发表了一篇长文。这篇文章中一半篇幅用来讲述佩雷尔曼的故事，另外一半则在讲哈佛大学数学家丘成桐以及两名中国数学家曹怀东和朱熹平。
曹怀东和朱熹平是摩根和田刚之外的另一个验证佩雷尔曼证明的团队。他们在 2006 年发表了一篇三百多页的论文，给出庞加莱猜想的完整证明。丘成桐随后在中国大陆召开记者会，宣布了这一消息。
曹怀东和朱熹平论文的摘要是这样写的：“在本文中，我们给出庞加莱猜想和几何化猜想的完整证明。这项工作依靠于过去 30 年里许多几何分析家的工作积累。该证明应被认为是汉密尔顿－佩雷尔曼 Ricci 流理论的至高成就。”
在一些人看来，这似乎在暗示汉密尔顿和佩雷尔曼只是做了基础性的工作，而证明庞加莱猜想的“临门一脚”是由这两位数学家做出来的。在《纽约客》的文章中，作者描绘了数学家们是如何想要从佩雷尔曼那里争功的。随后《纽约客》收到了丘成桐的律师函，函中称文章中存在“错误和诽谤内容”。
“我们在数学上从佩雷尔曼那里学到了东西。或许我们也应该暂停脚步，从佩雷尔曼对生活的态度上反思自己。”
2006 年，国际数学联合会决定授予佩雷尔曼菲尔兹奖。这是数学界的最高奖项，有人称它为数学界的诺贝尔奖。佩雷尔曼拒绝了。
国际数学联合会主席约翰·保尔（John Bal）飞去圣彼得堡，试图说服佩雷尔曼领奖。这是菲尔兹奖历史上没有出现过的情况，联合会主席竟然要亲自去说服一个获奖者接受这个奖项。他与佩雷尔曼交谈了数个小时，他向佩雷尔曼提供了几套方案，包括佩雷尔曼不必出席会议，他们把奖章送到圣彼得堡来。但是佩雷尔曼拒绝了。
格罗莫夫在一本书中回忆说，最初菲尔兹奖评审委员会给佩雷尔曼寄了封信，而佩雷尔曼表示，他不会与委员会对话。“一个人不应该跟委员会对话。”格罗莫夫说，“人应该跟人对话。……当委员会像机器一样运行的时候，你就应该停止跟它打交道——就是这么回事。唯一奇怪的事情就是越来越多的数学家不是这么做的。这才是奇怪的事情！”
那一年，本该是西班牙国王为佩雷尔曼颁奖。“国王是谁啊？”格罗莫夫说，“为什么国王能给数学家颁奖？他是谁？他什么都不是。在数学家的眼里，他什么都不是。”
另外也有人认为，佩雷尔曼拒绝菲尔兹奖的一个原因是，他需要与其他数学家分享这个奖项。根据规定，菲尔兹奖每次授予两到四个人。2006 年，与佩雷尔曼一同获奖的还包括俄罗斯数学家安德雷·欧克恩科夫（Andrei Okounkov）、美国加州大学的数学家陶哲轩、法国数学家温德林·沃纳（Wendelin Werner）。佩雷尔曼可能认为这些数学家所做的工作与他并不在一个层次上，所以不愿与他们并列。
2000 年，克雷数学研究所宣布了七个“千年难题”，并承诺有人解决任何一个难题，就奖励一百万美元。其实在所长詹姆斯·卡尔森（James Carlson）看来，此举的噱头意义更大，他只是想通过这样的方式来激发人们对数学的关注，并没有指望这些问题中的任何一个能够在他的有生之年中得到解决，也没想到百万美元真的能够发出去。
他完全没有料到的是，几年之后，佩雷尔曼就解决了其中的一个。同时，佩雷尔曼也为卡尔森出了道难题：佩雷尔曼不答应领奖。
于是，卡尔森像保尔那样也飞去了圣彼得堡。但是他没有卡尔森那样的运气——佩雷尔曼没有与他见面。他通过电话与佩雷尔曼交谈，怀着一线希望，希望佩雷尔曼能够接受这一百万美元。佩雷尔曼静静地听他讲。佩雷尔曼一直是一个有礼貌的人。最后佩雷尔曼告诉卡尔森，他需要考虑一下，如果决定领奖，会第一时间通知克雷研究所的。
现在看来，佩雷尔曼的回答只是出于礼貌，他从一开始就没有打算去领奖。
英国《每日邮报》今年 3 月份的报道说，佩雷尔曼紧闭家门，在屋内对外面采访的记者说：“我应有尽有。”
现在，佩雷尔曼与他的母亲生活在一起。自从他将一张鲁克辛转送的 CD 砸向这位少年时代的数学老师之后，他也与这位师友断绝了来往。
“如果他拒绝了（千禧数学奖），我并不会感到惊讶。”田刚在颁奖前对南方周末记者说。
“佩雷尔曼对公共场面和财富的厌恶令许多人迷惑不解。”瑟斯顿在颁奖仪式上说，“我没有跟他讨论过这个问题，也不能代表他发言，但是我想说，我对他内心的强大与清晰感到共鸣和敬仰。他能够了解和坚持真实。我们真实的需求位于内心深处，然而现代社会中的我们大多在条件反射式地不断地追逐财富、消费品和虚荣。我们在数学上从佩雷尔曼那里学到了东西。或许我们也应该暂停脚步，从佩雷尔曼对生活的态度上反思自己。”
（本文部分参考了 Masha Gessen 著《完美的严谨》（Perfect Rigor）一书，谨致谢忱。）
(In English)
Even among the "eccentrics" of the mathematical community, Grigori Perelman stands out as a peculiar one. On June 8th, a group of the world's most distinguished mathematicians gathered in Paris to present the Millennium Prize to the Russian mathematician. However, he was not present.
Previously, he had also declined the Fields Medal, the highest honor in mathematics. He once again forsook an honor coveted by others, along with a one-million-dollar prize.
Imagine you know nothing of the Earth's geography. You send out expeditions time and again, and these fleets successively discover new continents. The number of known continents grows to six. Yet, you're unsure if these are all the continents on Earth. You continue dispatching fleets, sending out hundreds of expeditions, but they find no more new landmasses. You then propose a conjecture: there are no more continents on Earth.
This conjecture seems reasonable, but it still requires proof. Then, Perelman appears. He demonstrates to you and the world, with perfect rigor, that there are indeed no more continents on Earth.
The above is an analogy from the Russian mathematician Mikhail Gromov. The real-life Grigori Perelman is not a geographer but a mathematician. The significance of his work in mathematics is no less than that of the analogy above – he constructed a beautiful proof confirming the correctness of the "Poincaré conjecture."
On June 8, some of the world's top mathematicians gathered at the Oceanographic Institute in Paris, near the Henri Poincaré Institute. "A century after Henri Poincaré's death, in the city where he lived and worked, the conjecture he bequeathed to us has been solved. Grigori Perelman is the climber who reached the summit of that three-dimensional world," said Michael Atiyah, a mathematician at the University of Edinburgh, in his speech praising Perelman.
The 81-year-old Atiyah is one of the most influential mathematicians of the 20th century and a recipient of the Fields Medal in 1966. However, he told Southern Weekly, "I don't know Perelman."
William Thurston, a mathematician at Cornell University, proposed a geometrization conjecture in the 1970s. He boldly stated at a conference in 1980 that his geometrization conjecture placed the Poincaré conjecture within a more comprehensive framework. He was quite optimistic that it would eventually be proven, but he didn't know if it would happen in his lifetime. He devoted a significant amount of energy to proving this conjecture himself, but without success.
"Perelman, with great interest and superb technique, constructed a beautiful proof where I and others had failed," Thurston said. "It's a proof I was unable to achieve: some of Perelman's strengths are precisely my weaknesses."
"I am honored to have this opportunity to publicly express my deep admiration and appreciation for Grigori Perelman," Thurston said in his speech. However, he also told Southern Weekly, "I haven't met Perelman, nor have I been able to attend his previous lectures."
More than ten world-class mathematicians presented the Millennium Prize to Perelman in Paris, yet most of them had never met or interacted with him. More importantly, Perelman himself was not present. This not only meant that Perelman disregarded an honor others could only dream of, but it also meant he forfeited a one-million-dollar prize.
"Perelman may have many reasons to refuse the prize, but I don't want to speculate," Gromov told Southern Weekly. "In fact, there's only one reason for him to accept it – money, but there are many reasons for him to refuse."
Gromov is one of the few mathematicians in the world who has had contact with Perelman. In fact, it was he who introduced the international mathematical community to the independent and unconventional mathematical genius from Russia.
In April 2003, Perelman arrived at the Massachusetts Institute of Technology (MIT) to begin his lecture tour of American universities.
The young Perelman lived in an imaginary world created with his mother's help, a world that contained little else besides mathematics.
Perelman was born in 1966 in the Soviet Union to a Jewish family. His mother was a mathematics teacher at a university. This seemed to provide a favorable condition for the development of his mathematical talent, but the widespread anti-Semitism in Soviet society also created a harsh environment for Perelman's growth and life.
How to explain the cruelty of life to a child is often a headache for parents. Perelman's mother chose a special approach – she presented the correct world in her mind as the real world to the young Perelman.
Therefore, in Perelman's world, anti-Semitism did not exist. This world persisted at least until his university years. Anti-Semitism that was obvious to any ordinary person did not hold up in Perelman's mind. This was largely related to Perelman's mathematical way of thinking. For example, Leningrad University only admitted two Jewish students each year, which could easily be considered a typical case of racial discrimination. However, in the year Perelman enrolled, he was granted an interview due to his medal in the International Mathematical Olympiad. Along with two other Jewish students who were admitted through exams, Leningrad University admitted three Jewish students that year. If the admission of only two Jewish students each year was proof of anti-Semitism, then perhaps in Perelman's view, the admission of three students that year was a counterexample to this proposition.
The ambiguous variables in social life were difficult for Perelman to understand, and this was formed in his childhood. His math club teacher, Sergey Rukshin, would take the train home with Perelman two evenings a week. In winter, Perelman would wear a Soviet-style fur hat with two flaps at the ears, which could be tied with a string to prevent the ears from freezing. Rukshin noticed that even in the warm train carriage, Perelman never untied the string. "He wouldn't just not take off his hat," Rukshin said in a book, "he wouldn't even untie the ear flaps, saying his mother would kill him if he did, because she told him not to untie the string, otherwise he would catch a cold."
Rukshin once criticized Perelman for not reading enough, believing his duty was not only to teach children mathematics but also literature and music. Perelman asked Rukshin why he should read those literature books. Rukshin told him it was because these books were "interesting," but Perelman's response was that the books that needed to be read should be listed on the school's required reading list.
Because of Perelman's personality, Rukshin, as a math competition coach, never worried about Perelman being "distracted" during math training. Perelman was indeed never distracted. When his classmates grew older and started kissing girls, Rukshin often caught them. But Perelman was never interested in girls.
Perelman lived in an imaginary world created with his mother's help, a world where rules were rules and contained little else besides mathematics. Rukshin was the most influential math coach for Perelman during his childhood, and Perelman became a part of Rukshin's life. He made Perelman's life in Leningrad safe and orderly, just like the world in Perelman's imagination, until he entered the specialized mathematics school No. 239.
Leningrad's specialized mathematics school No. 239 was founded by mathematician Andrei Kolmogorov. The mathematics education here differed from that of ordinary high schools. It taught mathematics in actual research while also tailoring instruction to students' backgrounds. It was also the only high school in the Soviet Union that taught ancient history. Students were also exposed to music, poetry, visual arts, and ancient Russian architecture. However, it did not offer other social science courses commonly found in Soviet schools.
In the micro-environment created by his teachers and school, Perelman remained isolated from the real world, and his own world was protected and preserved. When sitting in class with other mathematically gifted young people, Perelman always sat in the back. He remained silent, only speaking when he found someone's solution or explanation needed correction, and always decisively. Perhaps much of what was taught in class was useless to Perelman, but he would listen quietly, as he had always been a polite person because rules were rules.
Another of Perelman's principles was that he had to tell the complete truth, otherwise, he might consider it political. During the All-Union Mathematical Olympiad, each student was given a problem. Whoever solved it would raise their hand to signal the teacher, who would then take them outside the classroom. The student would explain their solution to the teacher. If correct, the teacher would give them the next problem. If incorrect, they would go back and continue working on the same problem. The final result was determined by who solved the most problems within the allotted time. Once, Perelman solved a problem, and the teacher called him outside. After he explained it to the teacher, the teacher said "correct" and turned to go back into the classroom. But Perelman stopped the teacher, saying there were three other possible outcomes for the problem! He insisted on telling the teacher all the possibilities, even though it was a waste of time for the math competition.
By the final year of high school, Perelman had already won a gold and a silver medal in the All-Union Mathematical Olympiad and ultimately won a gold medal with a perfect score of 42 in the 1982 International Mathematical Olympiad.
The proof of the "Soul Conjecture" made Perelman a young star in the mathematical world. To everyone's amazement, it only took him four pages.
In 1991, Gromov helped Perelman attend the Geometry Festival on the East Coast of the United States. Prior to this, Perelman had studied at Leningrad University for six years, during which time he chose to develop in the direction of geometry.
The Geometry Festival was an annual mathematics conference, held that year at Duke University. Perelman was one of seven speakers at the Geometry Festival, and he presented a talk titled "Alexandrov Spaces with Curvature Bounded Below." The paper on this topic was published a year later and became one of his representative works.
During the Geometry Festival, Gromov introduced Perelman to various important figures, which led to Perelman obtaining the opportunity to do postdoctoral work in the United States.
Jeff Cheeger was a mathematician at the Courant Institute of Mathematical Sciences at New York University, and he also had a presentation at that year's Geometry Festival. He noticed Perelman. He met with Perelman after being introduced by Gromov. A year later, in the fall of 1992, Perelman arrived at the Courant Institute to begin his postdoctoral work.
Even among the "eccentrics" of the mathematical community, Perelman stood out as a peculiar one. He seemed to always wear the same clothes, had a scruffy beard, and didn't cut his nails – he believed that was the natural state of nails. His diet consisted only of bread and yogurt. American bread probably didn't taste good to him, but fortunately, he found a store that sold authentic Russian bread and often walked a considerable distance to buy it. Therefore, he had few expenses, and he kept all his stipends in the bank (which saved him a sum of money, ensuring he could live comfortably in Russia for a period of time later).
Perelman never left his mother throughout his life. During his postdoctoral period in New York, his mother came to the United States with him, living in Brooklyn and taking care of Perelman's daily life.
We don't know how many friends Perelman had in his lifetime, but it's safe to say the number was very small. During his time at New York University, he made a rare friend. Perelman's teacher, Viktor Zalgaller, was very certain of this. His friend was Gang Tian, now a mathematics professor at Princeton University and Peking University.
At that time, Perelman often talked with Tian. However, in Tian's memory, their conversations were solely about mathematics itself, never touching on other matters. He believed Perelman might chat about other topics with some other friendly person, but not with him. Tian knew that Perelman would go to a place near the Brooklyn Bridge to buy bread, but since Tian himself didn't care about eating this or that kind of bread, he didn't know what was so special about the bread Perelman liked.
In 1993, Perelman solved a long-standing problem in mathematics – the "Soul Conjecture." This conjecture was proposed by Cheeger and another mathematician. Over the course of twenty years, some had written lengthy papers analyzing this problem but could only provide partial proofs. Perelman provided a complete proof that amazed everyone – and it only took him four pages!
The proof of the "Soul Conjecture" made Perelman a young star in the mathematical world. He was only 27 years old that year. In the fall of the same year, he moved to the University of California on the West Coast to continue his research. However, Perelman began to experience mathematical failure, which was likely the first failure of his life. He got stuck in his research on Alexandrov spaces and made no progress. 1994 was probably a year full of frustration for him. Later, no one knew what he was researching until eight years later when he suddenly posted his proof of the Poincaré conjecture on the internet.
After solving a series of famous problems in the 1990s, he "disappeared." Now he has resurfaced.
On November 12, 2002, Michael Anderson, a mathematician at the State University of New York, suddenly received an email from Perelman. At this time, Perelman had been back in Russia for many years. In the email, Perelman simply wrote: "I would like to draw your attention to my paper arxiv.org/abs/math/0211159 , posted in ArXiv." Then it was a copy of the abstract of the paper.
Anderson was one of a dozen mathematicians who received the same email. These mathematicians were all people who had studied the Poincaré conjecture from different angles over the years. At 5:38 am the next day after receiving the email (it seems he likely read Perelman's paper overnight), Anderson sent emails to other mathematicians, hoping they could help assess the reliability of this paper. "It seems to me that the ideas in the paper are new and original – typical Grisha [Perelman's nickname] style," Anderson wrote in the email. He also said: "He solved a series of famous problems in other areas in the 1990s, and then 'disappeared.' Now it appears he has resurfaced."
ArXiv is a website run by the Cornell University Library for scientists in mathematics and physics to post preprints of their papers. The paper Perelman posted was the first of three articles in his proof of the Poincaré conjecture. The second and third articles were posted in 2003. The entire process flowed smoothly, but it would take his peers one or two years to understand these three articles.
In April 2003, Perelman arrived at MIT to begin his lecture tour of American universities. Even for a mathematician as quiet, introverted, and low-key as he was, he couldn't contain his eagerness to share his work with others, giving lectures every day at seminars to different audiences. Perelman patiently explained his proof step by step and was happy to answer every question from the audience. Of course, this sharing was limited to the mathematical circle. He only wanted to explain it to those who could potentially understand his work.
However, a reporter from The New York Times caught wind of this information and published a report in the newspaper titled "Russian Claims Solution to a Famous Math Problem." This report likely displeased Perelman. First, he didn't "claim" anything; he was simply discussing it with his peers. More importantly, the report mentioned that if Perelman's proof withstood two years of scrutiny from his peers, he might receive a one-million-dollar prize, the Millennium Prize from the Clay Mathematics Institute. This wording gave the false impression that Perelman was motivated by the prize money. In fact, Perelman had already begun working on proving the Poincaré conjecture long before the Clay Mathematics Institute established the million-dollar prize.
Around this time, Perelman's friend, Tian, also made a "mistake." In the spring of 2004, Tian was interviewed by the American magazine Science about Perelman's work. Afterward, he found that Perelman no longer responded to his emails.
In fact, Perelman's paper was also an important direction for Tian's research. He and another topologist, John Morgan, formed one of the three teams in the world verifying Perelman's proof.
"Between 2002 and 2006, apart from his time at MIT, we had some contact on mathematical matters. During his visit to MIT, we talked a lot, mostly about mathematics," Tian recalled. "In the many years after he returned to Russia, we had almost no contact."
No one knows exactly why Perelman stopped responding to his old friend, but he seemed to have done it thoroughly. Morgan and Tian wrote a book about their research results and sent it to Perelman by mail. But after a while, the mail was returned to them.
Tian explained this to Southern Weekly: "After the book was completed, we did send it to a few people who might be interested, including Perelman. Given that his work was directly related, we sent him a copy to see if he could provide any comments. This is a standard practice. But the manuscript was returned, saying the address was incorrect. We didn't think too much about it. Maybe we didn't write the address correctly."
He cut off all contact with the outside world. Meanwhile, the outside world was full of curiosity about him, and countless media began to surround his home.
If there is anyone in the world who has the authority to evaluate Perelman's work, it should be Richard Hamilton, a mathematics professor at Columbia University. Hamilton's most famous contribution to mathematics is the discovery of Ricci flow, which was the assistant that brought Perelman close to the summit.
For many years before Perelman published his paper, Hamilton himself, and the so-called "Ricci flow community" that formed around him, had also been trying to prove the Poincaré conjecture, but without success. During this time, it is questionable whether Hamilton even knew about Perelman. Perelman had once attended Hamilton's lectures and actually held Hamilton in high regard. He even asked Hamilton questions after the lectures. At that time, Hamilton seemed friendly and approachable.
However, when Perelman, a stranger outside the "Ricci flow community," arrived in the United States with his answer and gave lectures everywhere, Hamilton remained silent. As the person who should have been there the most, he did not appear at the lectures soon. Only when Perelman's lecture tour reached Columbia University did Hamilton finally appear in the classroom. After listening to Perelman's explanation, he simply asked a few questions; in Perelman's view, these questions lacked depth, and perhaps he hadn't even finished reading his paper.
In May 2004, Perelman returned to Saint Petersburg. He took a walk with Rukshin, his math teacher from his youth, and told him he was disappointed with the mathematical community. In December 2005, without a clear reason, Perelman resigned from his position at the Steklov Institute of Mathematics in Moscow.
Thus, Perelman once again "disappeared" from the world. Perelman cut off all contact with the outside world. He only talked to his mother and his teacher, Rukshin, on a regular basis. Meanwhile, the outside world was full of curiosity about Perelman. Since the birth of this world-class mathematical star in Russia, countless Russian media began to surround his home.
"As long as I am not conspicuous, I have a choice," Perelman once said. "Either to make something ugly or, if I don't do this, I will be treated as a pet. Now, I am a conspicuous person, I cannot stay a silent pet. This is why I quit."
Perelman not only quit his job, but he actually withdrew from the mathematical community.
Among all the outsiders, two authors from The New Yorker were fortunate. They became the only journalists in the world who had talked with Perelman himself for several hours.
In June 2006, they flew to Saint Petersburg. Before that, they had sent several emails to Perelman's email address, hoping he could arrange a meeting. As expected, they received no reply. After arriving in Saint Petersburg, they took a taxi to Perelman's apartment.
They didn't knock on the door but left a book – a collection of John Nash's works – in Perelman's mailbox, along with a note telling Perelman they would be waiting for him the next afternoon on a bench in a nearby playground. The next day, the two authors waited on the bench all afternoon, but Perelman did not show up.
So, the two left a box of pearl milk tea and another note in Perelman's mailbox, listing the questions they wanted to discuss with him. Perelman still did not respond. They repeated this process once more. Perelman still did not respond.
So, the two thought Perelman was not at home. They rang the doorbell, hoping to at least talk to Perelman's mother. A woman opened the door and let them into the house. Perelman was inside. After greeting Perelman, the two authors learned that he hadn't checked his email in months and hadn't opened his mailbox in a week, so he had no idea who these two were.
The next day, Perelman walked around the streets of Saint Petersburg with these two uninvited guests for four hours and then watched a five-hour vocal competition together. He repeatedly told them he was no longer in the mathematical community and did not consider himself a professional mathematician. He also told them, "I want to make some friends, they don't have to be mathematicians."
The two authors returned to the United States and published a long article in The New Yorker. Half of this article was devoted to telling Perelman's story, and the other half was about Harvard mathematician Shing-Tung Yau and two Chinese mathematicians, Huai-Dong Cao and Xi-Ping Zhu.
Cao and Zhu were another team verifying Perelman's proof, besides Morgan and Tian. They published a paper of over three hundred pages in 2006, providing a complete proof of the Poincaré conjecture. Yau subsequently held a press conference in mainland China to announce this news.
The abstract of Cao and Zhu's paper reads: "In this paper, we give a complete proof of the Poincaré conjecture and the geometrization conjecture. This work depends on the accumulation of the work of many geometric analysts over the past thirty years. This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow."
Some people interpreted this as suggesting that Hamilton and Perelman had only done the foundational work, and the "final touch" in proving the Poincaré conjecture was made by these two mathematicians. In The New Yorker article, the authors described how mathematicians tried to take credit from Perelman. Subsequently, The New Yorker received a letter from Yau's lawyer, claiming that the article contained "false and defamatory statements."
"We have learned something from Perelman in mathematics. Perhaps we should also pause and reflect on ourselves from Perelman's attitude towards life."
In 2006, the International Mathematical Union decided to award Perelman the Fields Medal. This is the highest award in mathematics, sometimes called the Nobel Prize of mathematics. Perelman refused it.
The president of the International Mathematical Union, John Ball, flew to Saint Petersburg to try to persuade Perelman to accept the award. This was unprecedented in the history of the Fields Medal – the president had to personally persuade a recipient to accept the award. He talked with Perelman for several hours and offered Perelman several options, including that Perelman did not need to attend the conference, and they would deliver the medal to Saint Petersburg. But Perelman refused.
Gromov recalled in a book that the Fields Medal selection committee initially sent Perelman a letter, and Perelman indicated that he would not have a dialogue with the committee. "One should not have a dialogue with a committee," Gromov said. "One should have a dialogue with people. ... When a committee operates like a machine, you should stop dealing with it – that's it. The only strange thing is that more and more mathematicians are not doing this. That's the strange thing!"
That year, the King of Spain was supposed to present the award to Perelman. "Who is the king?" Gromov said. "Why can a king present an award to a mathematician? Who is he? He is nothing. In the eyes of a mathematician, he is nothing."
Others believe that one reason Perelman refused the Fields Medal was that he would have to share the award with other mathematicians. According to the rules, the Fields Medal is awarded to two to four people each time. In 2006, along with Perelman, the award was also given to Russian mathematician Andrei Okounkov, American mathematician Terence Tao from the University of California, and French mathematician Wendelin Werner. Perelman may have felt that the work of these mathematicians was not on the same level as his, so he was unwilling to be ranked alongside them.
In 2000, the Clay Mathematics Institute announced the seven "Millennium Prize Problems" and promised to award one million dollars to anyone who solved any of them. In fact, in the eyes of the institute's director, James Carlson, this move was more of a gimmick. He simply wanted to use this method to stimulate people's interest in mathematics. He didn't expect any of these problems to be solved in his lifetime, nor did he expect the million dollars to actually be awarded.
He completely didn't anticipate that a few years later, Perelman would solve one of them. At the same time, Perelman also presented Carlson with a difficult problem: Perelman refused to accept the award.
So, Carlson, like Ball, flew to Saint Petersburg. But he didn't have Carlson's luck – Perelman did not meet with him. He talked with Perelman on the phone, holding onto a glimmer of hope that Perelman might accept the one million dollars. Perelman listened to him quietly. Perelman had always been a polite person. Finally, Perelman told Carlson that he needed to think about it and would notify the Clay Mathematics Institute as soon as possible if he decided to accept the award.
It now seems that Perelman's answer was simply out of politeness. He had no intention of accepting the award from the beginning.
A report in the British Daily Mail in March of this year said that Perelman closed his door tightly and told reporters outside, "I have everything."
Now, Perelman lives with his mother. He has also cut off contact with Rukshin, his math teacher and friend from his youth, after smashing a CD that Rukshin had given him.
"If he refuses [the Millennium Prize], I won't be surprised," Tian told Southern Weekly before the award ceremony.
"Perelman's aversion to public appearances and wealth puzzles many," Thurston said at the award ceremony. "I haven't discussed this issue with him, and I can't speak for him, but I want to say that I resonate with and admire the strength and clarity of his inner self. He is able to understand and adhere to the truth. Our real needs lie deep within, yet most of us in modern society are constantly chasing after wealth, consumer goods, and vanity in a conditioned reflex. We have learned something from Perelman in mathematics. Perhaps we should also pause and reflect on ourselves from Perelman's attitude towards life."
(This article partially references Masha Gessen's book "Perfect Rigor," to which sincere gratitude is expressed.)