约翰·纳什:与疯狂博弈的孤独天才

他是天才，21岁就提出“纳什均衡”，为博弈论研究带来全新突破。他也是疯子，曾因罹患精神分裂症而被迫中止学术研究。他很不幸，刚成为数学界的耀眼新星便被病魔击倒，人生陷入一片黑暗。他也很幸运，尽管疯癫古怪，却从未被家人和朋友抛弃，总能得到庇护和帮助。1994年10月，约翰・纳什获得诺贝尔经济学奖，这位一直在与病魔博弈的孤独天才终于得到了应得的认可。2015年5月23日，纳什因车祸离世，天才陨落，只留下世人的声声叹息。

Several weeks before the 1994 Nobel Prize in economics was announced on Oct. 11， two mathematicians―Harold W. Kuhn and John Forbes Nash Jr.―visited their old teacher， Albert W. Tucker， at Meadow Lakes1）， a nursing home near Princeton.

When Mr. Nash stepped out of the room， Mr. Kuhn returned to tell Mr. Tucker a stunning secret： Unbeknownst to Mr. Nash， the Royal Swedish Academy intended to grant Mr. Nash a Nobel for work he had done as the old man’s student in 1949， work that turned out to have revolutionary implications for economics. 康复后的纳什

The award was a miracle. It wasn’t just that Mr. Nash， one of the mathematical geniuses of the postwar era， was finally getting the recognition he deserved. Nor that he was being honored for a slender 27-page Ph.D. thesis written almost half a century ago at the tender age of 21.

The real miracle was that the 66-year-old Mr. Nash―tall， gray， with sad eyes and the soft， raspy2） voice of someone who doesn’t talk much―was alive and well enough to receive the prize. For John Nash was stricken with paranoid schizophrenia3） more than three decades earlier.

Mr. Nash’s terrible illness was an open secret among mathematicians and economists. No sooner had Fortune magazine singled him out4） in July 1958 as America’s brilliant young star of the “new mathematics” than the disease had devastated Mr. Nash’s personal and professional life. He hadn’t published a scientific paper since 1958. He hadn’t held an academic post since 1959.

His life， once so full of brightness and promise， became hellish5）. There were repeated commitments to psychiatric hospitals. Failed treatments. Fearful delusions. A period of wandering around Europe. Stretches6） in Roanoke， Va.， where Mr. Nash’s mother and sister lived. Finally， a return to Princeton， where he had once been the rising star.

Starting Out：

The First Signs of Genius

John Nash’s West Virginia roots are often invoked by people who knew him at Princeton or at the Massachusetts Institute of Technology， where he taught for a while in the 50’s， to explain his lack of worldliness. But Bluefield， the town where he grew up， was hardly a backwater7）.

Mr. Nash’s mother， Margaret， was a Latin teacher. His father， John Sr.， was a gentlemanly electrical engineer. Nothing was more important to the senior Nashes than supervising their children’s education， recalls the sister， Martha Nash Legg. John Jr. was a prodigy8） but not a straight-A student. He read constantly. He played chess. He whistled entire Bach melodies. “John was always looking for a different way to do things，” said Mrs. Legg， “He could see ways to solve problems that were different from his teacher’s.”

In the fall of 1945， Mr. Nash enrolled at Carnegie-Mellon， then Carnegie Tech， in Pittsburgh. It was there that the label “genius” was first applied to Mr. Nash. His mathematics professor called him “a young Gauss9）” in class one day. Mr. Nash switched from chemistry to math in his freshman year. Two years later he had a B.S. and was studying for an M.S.

His graduate professor， R. J. Duffin， recalls Mr. Nash as a tall， slightly awkward student who came to him one day and described a problem he thought he had solved. Professor Duffin realized with some astonishment that Mr. Nash， without knowing it， had independently proved Brouwer’s famed theorem10）. The professor’s letter of recommendation for Mr. Nash had just one line： “This man is a genius.”

Making Waves： Game Theory and More

In 1948， the year Mr. Nash entered the doctoral program at Princeton with a fellowship11）， the town was arguably the center of the mathematical and scientific universe. At once eager to prove himself and12） somewhat gauche13）， especially compared with older students who had served in the war， Mr. Nash quickly became one of the brilliant young men who performed mental pyrotechnics14） in the common room of Fine Hall15）.

Other students found him a loner， odd as well as brilliant. When he wasn’t in the common room talking a blue streak16）， he paced. Around and around he would go， following Fine Hall’s quadrangular17） hallways， occasionally dashing into empty classrooms to scribble， with lightning speed， on blackboards. “He was always an unusual person，” said Jack Milnor， an undergraduate at the time and now a mathematician at the State University of New York at Stony Brook. “He tended to say whatever came into his mind.”

Mr. Nash’s Nobel-winning thesis on game theory was the product of his second year at Princeton. Game theory was the invention of von Neumann18） and a Princeton economist named Oskar Morgenstern. Their 1944 book， The Theory of Games and Economic Behavior， was the first attempt to derive logical and mathematical rules about rivalries.

Briefly， von Neumann only had a good theory for pure rivalries in which one side’s gain was the other’s loss. Mr. Nash focused on rivalries in which mutual gain was also possible. He showed that there were stable solutions―no player could do better given what the others were doing―for such rivalries under a wide variety of circumstances. In doing so， he turned game theory， a beguiling19） idea， into a powerful tool that economists could use to analyze everything from business competition to trade negotiations. “It wasn’t until Nash that game theory came alive for economists，” said Robert Solow， a Nobel laureate in economics at M.I.T.

Mr. Nash got his doctorate on his 22nd birthday， June 13， 1950. After brief interludes as an instructor at Princeton and as a consultant at the Rand Corporation20）， the Cold War think tank， Mr. Nash moved on to teach at M.I.T. in 1951.

The Disease： “It’s All Over for Him”

By the mid-1950’s， Mr. Nash was phenomenally productive. When he got tired of mathematicians， he would wander over to the economics department to talk to Mr. Solow and another Nobel laureate， Paul Samuelson.

And it was during this period that Mr. Nash met his future wife， Alicia Larde， an El Salvadoran physics student at M.I.T. who took advanced calculus from him. Small， graceful， with extraordinary dark eyes， Alicia looked like an Odile21） in Swan Lake. “He was very， very good looking， very intelligent，” Mrs. Nash recalls. “It was a little bit of a hero worship thing.” They were married in 1957， a year Mr. Nash spent on leave at the Institute for Advanced Study.

By the time the Nashes returned to M.I.T.， John Nash had been awarded tenure. Mrs. Nash went back to graduate school and worked part time in the computer center. In the fall of 1958， she became pregnant with their son， John Charles Martin Nash. “It was a very nice time of my life，” she recalled.

It is just then， when life seemed so very sweet， that John Nash got sick. Within months， at age 30 in the spring of 1959， Mr. Nash was committed to McLean Hospital， a psychiatric institution in Belmont， Mass.

In the months leading up to his hospitalization， Mr. Nash became another person. He skipped from subject to subject. Some of his lectures no longer made sense. He fled to Roanoke at one point， abandoning his classes. He wrote strange letters to various public figures.

“It was very sad，” said Professor Shapley at U.C.L.A.， who ran into Mr. Nash from time to time. “There was no way to talk to him or even follow what he was saying.”

In any event， Mr. Nash’s paranoia intensified and he could no longer work. After resigning his M.I.T. post， he went to Europe， wandering from city to city. He feared he was being spied on and hunted down and he tried to give up his United States citizenship. His wife and colleagues began to receive postcards with odd messages， many concerning numbers. Eventually， the Nashes separated and he moved to Roanoke to live with his mother.

The Abyss： Two Decades of Darkness

For most of the next 20 years， Mr. Nash divided his time between hospitals， Roanoke and， increasingly， Princeton.

In 1963， Mrs. Nash divorced him but eventually let him live at her house. Mr. Nash was hospitalized at least three more times. Mrs. Nash， who never remarried， supported her former husband and her son by working as a computer programmer， with some financial help from family， friends and colleagues.

Mr. Nash became a sad， ghostly presence around Princeton and a mysterious character， the Phantom of Fine Hall. “Everyone at Princeton knew him by sight，” recalls Daniel R. Feenberg， a Princeton graduate student in the 1970’s and now an economist at the National Bureau of Economic Research. “His clothes didn’t quite match. He looked vacant22）. He was mostly silent. He was around a lot in the library reading books or walking between buildings.”

Alicia Nash believed very firmly that Mr. Nash should live at home and stay within Princeton’s mathematics community even when he was not functioning well. Martha Legg applauds her decision. “Being in Princeton was good for him，” said Mrs. Legg. “In a place like Princeton， if you act strange， you’re special. In Roanoke， if you act strange， you’re just different. They didn’t know who he was here.”

Some former colleagues at Princeton and M.I.T. tried to help with jobs on research projects， though very often Mr. Nash couldn’t accept the help. Professor Shapley at U.C.L.A. succeeded in getting a cash mathematics prize for Mr. Nash in the 70’s. There were other forms of kindness， like getting Mr. Nash access to university computers or remembering to invite him to seminars when old friends turned up on campus.

Coming Back： Finally， a Remission

Still， the people who stayed in regular contact with him eventually came to believe that his illness would never end. Then came what Professor Kuhn calls “a miraculous remission.” And as happens， for reasons unknown， in the case of some people with schizophrenia， it was not， according to Mrs. Nash or Mrs. Legg， due to any drug or treatment. “It’s just a question of living a quiet life，” said Mrs. Nash. The most dramatic sign of that remission， perhaps， is that Mr. Nash was able to do mathematics again.

And now Mr. Nash is a Nobel laureate. The story of his prize is itself testament not only to his survival but to the fierce loyalty and admiration he inspired in others. During the 20-plus years of Mr. Nash’s illness， game theory flourished and it is hard to find an important article in the field that doesn’t refer to his work. “The truths Nash discovered were all very surprising，” said Simon Kochen， another Princeton mathematician. “Nash is a man who surprises people.”

在1994年10月11日揭晓年度诺贝尔经济学奖揭晓数周之前（编注：英文原文发表于1994年11月，纳什获得诺奖后不久），哈罗德・W・库恩和小约翰・福布斯・纳什这两位数学家来到距普林斯顿大学不远的梅多湖养老院，看望他们昔日的老师艾伯特・W・塔克。

纳什离开房间后，库恩又折回来告诉了塔克老师一个惊人的秘密：瑞典皇家科学院准备授予纳什诺贝尔奖，以表彰1949年纳什在塔克老师门下学习时所做的研究―这些研究后被证实对经济学有革命性的影响，而纳什对这个消息还一无所知。

纳什此番获奖是一个奇迹。这不仅是因为纳什―这位战后时期的数学天才之一终于获得了他应得的认可，也不仅是因为令他获奖的是他在近半个世纪之前以21岁的弱冠之龄写下的寥寥27页的博士论文。

真正的奇迹在于，时年66岁的纳什―高高的个子，头发灰白，眼神忧郁，有着沉默寡言者的温柔、沙哑的嗓音―依然康健，还能够领奖。因为在30多年前，约翰・纳什患上了妄想型精神分裂症。

纳什所患的可怕疾病在数学家和经济学家当中是个公开的秘密。1958年7月，纳什被《财富》杂志评为美国“新数学”领域的耀眼新星，此后不久，疾病就摧毁了他的个人生活和职业生涯。自1958年起，他再未发表过学术论文。自1959年起，他再未担任过学术职务。

他的人生一度充满光明，前途似锦，后来却变得如地狱般黑暗。他屡次被送进精神病院，经历失败的治疗，忍受着可怕的妄想。曾有一段时间，他在欧洲四处游荡，还曾多次在母亲和妹妹所居住的弗吉尼亚州的罗阿诺克住上一阵子。最终，他回到了普林斯顿―他曾作为一颗新星冉冉升起的地方。

起步阶段：天资初露

20世纪50年代，纳什曾在普林斯顿大学和麻省理工学院短暂任教，那里认识纳什的人常用他的西弗吉尼亚出身来解释他的不谙世事。不过，布卢菲尔德这个他从小长大的小镇可算不上穷乡僻壤。

纳什的母亲玛格丽特是名拉丁文教师。他的父亲老约翰是个温文尔雅的电气工程师。据纳什的妹妹玛莎・纳什・莱格回忆，对老纳什夫妇而言，没有什么比监督孩子们的教育更重要的了。小约翰是个神童，但不是全优生。他总是在看书，会下国际象棋，能用口哨吹出整支巴赫的曲子。“约翰总是在寻找做事情的不同方法，”莱格夫人说，“他能找到跟老师不一样的解题方法。”

1945年秋，纳什在匹兹堡的卡内基-梅隆大学（当时叫卡内基技术学院）登记入学。正是在那里，纳什第一次被贴上“天才”的标签。他的数学教授有一天在课堂上称他为“小高斯”。大一那年，纳什从化学系转到数学系，两年后取得理学学士学位，并继续攻读理学硕士学位。

他读研究生时的教授R.J.达芬回忆说，当时的纳什是个个子高高、稍显拘束的学生。有一天，纳什来找他，跟他描述了一道难题，纳什觉得自己解开了这道题。达芬教授不无惊愕地发现，纳什独立证明了布劳威尔的著名定理，而纳什自己还不知情。达芬教授为纳什所写的推荐信只有一句话：“此人是个天才。”

引起轰动：博弈论及其他

1948年，纳什获得奖学金，进入普林斯顿大学攻读博士学位。当时的普林斯顿可以说是数学界和科学界的中心。纳什既渴望证明自己，又有些不善交际（这一点与那些曾经入伍参战的年龄较大的同学比起来尤为明显）。他很快就成了才华横溢的年轻学子中的一员，他们常在数学系大楼的公共休息室里展示自己超群的智慧。

同学们觉得纳什性格孤僻，既聪明又古怪。他不是在公共休息室里滔滔不绝地演讲，就是在踱步。他会沿着数学系大楼四边形的走廊一圈圈地走，偶尔冲进一间空着的教室，在黑板上飞快地写写画画。“他一直是个不同寻常的人，”当年的本科生、现在的纽约州立大学石溪分校的数学家杰克・米尔诺说，“他常常想到什么就说什么。”

令纳什赢得诺贝尔奖的论文是关于博弈论的，论文于他在普林斯顿求学的第二年写就。博弈论的创始者是冯・诺依曼和普林斯顿大学一位名叫奥斯卡・莫根施特恩的经济学家。他们在1944年出版了著作《博弈论与经济行为》，首次尝试从竞争关系中推导出逻辑和数学法则。

简单地说，冯・诺依曼只是针对纯粹的竞争提出了一个不错的理论，在这种竞争中，一方的获益就是另一方的损失。纳什的研究则聚焦于也可能出现双赢的竞争。他向人们表明，在各种不同的情况下这种竞争都存在稳定的解决方案：考虑到其他参与博弈者的行为，参与博弈的各方都不会更占上风。如此一来，他就把博弈论从一种有趣的想法变成了一件强大的工具，经济学家们可以用它来分析从商业竞争到贸易谈判的种种问题。“直到纳什出现，博弈论才为经济学家们灵活运用。”麻省理工学院的诺贝尔经济学奖得主罗伯特・索罗说道。

1950年6月13日是纳什22岁生日，当天他获得了博士学位。他在普林斯顿做了一段时间的讲师，又在冷战时期的智库兰德公司担任了一段时间的顾问。两次短暂任职之后，纳什于1951年前往麻省理工学院任教。

疾病来袭：“他完了”

20世纪50年代中期以前，纳什在学术上成绩斐然。和数学家们待腻了的时候，他会信步走到经济学系，同索罗及另一位诺贝尔奖得主保罗・萨缪尔森交谈。

就是在这一时期，纳什结识了他未来的妻子―麻省理工学院物理系的萨尔瓦多裔学生艾里西亚・拉德。艾里西亚是纳什所授高等微积分课上的学生。她身材娇小，举止优雅，有一双乌黑的眼睛，就像《天鹅湖》中的奥黛尔一样。“他非常非常帅，人很聪明，”纳什夫人回忆道，“我对他的感觉有点像对英雄的崇拜。”他们于1957年结婚，那一年，纳什从麻省理工的高等研究院请了一年的假。

待到纳什夫妇回到麻省理工学院时，纳什已经取得了终身教职。纳什夫人回到研究生院继续学业，并在计算机中心做兼职工作。1958年秋，她怀上了他们的儿子约翰・查尔斯・马丁・纳什。“那是我人生中非常美好的一段时光。”她回忆说。

正当生活看起来如此甜蜜之时，约翰・纳什病了。不出几个月，在1959年的春天，30岁的纳什被送进了麦克莱恩医院，这是位于马萨诸塞州贝尔蒙特的一家精神病院。

在入院前的几个月里，纳什完全变了个人。他说话时从一个话题跳到另一个话题。有时他讲的有些课完全让人不知所云。他一度抛下教书的工作，跑到罗阿诺克。他给许多公众人物写过内容古怪的信。

“这让人很难过，”当年不时遇见纳什的加州大学洛杉矶分校的沙普利教授说，“完全没法与他交谈，甚至听不懂他在说什么。”

总之，纳什的妄想症加重了，他无法再继续工作。他辞去了麻省理工学院的教职，之后去了欧洲，在不同的城市游荡。他担心自己正在被监视、追踪，试图放弃自己的美国公民身份。他的妻子和同事开始收到内容怪异的明信片，其中许多都与数字有关。最终，纳什夫妇分居了。纳什搬到罗阿诺克和母亲住在一起。

坠入深渊：20年的黑暗岁月

在随后的20年里，纳什的大部分时间是在医院、罗阿诺克和普林斯顿度过的。他在普林斯顿待的时间越来越长。

1963年，纳什夫人与他离婚，但最终同意让他继续住在家里。纳什至少又住过三次院。纳什夫人没有再婚，依靠做计算机程序员的收入以及家人、朋友和同事们的一些接济来养活前夫和儿子。

纳什成了普林斯顿一个令人难过的游魂和神秘人物，成了数学系大楼的幽灵。“普林斯顿的每一个人看到他的样子都知道是他，”20世纪70年代在普林斯顿读研究生、如今是美国国家经济研究局经济学家的丹尼尔・R・芬伯格回忆道，“他衣服不太搭，看上去神情茫然，大多数时候都默不作声。他经常在图书馆读书，或是在各个大楼间徘徊。”

艾里西亚・纳什坚信，即使在不太能正常生活和工作的情况下，纳什也应该住在家里，并待在普林斯顿的数学圈子里。玛莎・莱格赞成她的决定。“待在普林斯顿对他有好处，”莱格夫人表示，“在普林斯顿那样的地方，如果你举止怪异，那表示你特别。而在罗阿诺克，你要是举止怪异，那你就是另类。这里的人们可不知道他是谁。”

普林斯顿和麻省理工学院的一些前同事试着帮助纳什，为他提供过一些研究工作。不过，通常纳什没法接受这些帮助。20世纪70年代，加州大学洛杉矶分校的沙普利教授成功地为纳什争取到了一项数学奖的现金奖励。人们还以其他方式表达着善意，比如允许纳什使用学校的计算机，或是在老朋友来学校时邀请他一起参加研讨会。

病后回归：病情终于缓解

然而，那些经常与他保持联系的人最终还是认为，他的病永远不会好了。但是接下来就出现了库恩教授所称的“奇迹般的缓解”。据纳什夫人和莱格夫人称，就像在有些精神分裂症患者身上所发生的那样，这次不明原因的好转不是任何药物或疗法的功效。“关键就是要平静地生活。”纳什夫人说。这次病情缓解最突出的标志或许就是纳什又能研究数学了。

如今，纳什是诺贝尔奖的获得者。他获奖这件事本身就是一种证明，不仅证明他战胜了疾病，而且证明他在人们心中激发起了强烈的忠诚和崇敬之情。在纳什患病的20多年里，博弈论蓬勃发展，在该领域的重要论文中，你很难发现有哪一篇论文是没引用他的研究成果的。“纳什发现的原理非常惊人，”另一位普林斯顿大学的数学家西蒙・柯晨表示，“纳什是那种能让人大吃一惊的人。”

1. Meadow Lakes：梅多湖养老院，美国一个持续照料退休社区（Continuing Care Retirement Community，简称CCRC），为老年人提供自理、介护、介助一体化的居住设施和服务。

2. raspy [?r?spi] adj. 声音嘶哑的;刺耳的

3. paranoid schizophrenia：妄想型精神分裂症

4. single out：（从一群人中）选出，挑出

5. hellish [?hel??] adj. 地狱般的

6. stretch [stret?] n. 一段时间;一阵子

7. backwater [?b?k?w??t?（r）] n. 穷乡僻壤;落后地区

8. prodigy [?pr?d?d?i] n. 奇才;天才;神童

9. Gauss：即约翰.卡尔.弗里德里希.高斯（1777～1855），德国著名数学家、物理学家、天文学家、大地测量学家，近代数学奠基者之一

10. 此处指布劳威尔不动点定理，是拓扑学里一个非常重要的不动点定理。

11. fellowship [?fel????p] n. （发给大学研究生的）奖学金

12. at once … and …：既……又……

13. gauche [???] adj. 不善交际的;笨拙的

14. pyrotechnics [?pa?r???tekn?ks] n. 出色的表现;（本领的）炫示

15. Fine Hall：此处指普林斯顿大学的数学系大楼。

16. talk a blue streak：滔滔不绝地讲话

17. quadrangular [kw??dr??j?l?（r）] adj. 四边形的

18. von Neumann：即约翰.冯.诺依曼（1903～1957），20世纪最重要的数学家之一，在现代计算机、博弈论和核武器等诸多领域颇有建树，被称为“计算机之父”和“博弈论之父”。

19. beguiling [b??a?l??] adj. 迷人的

20. Rand Corporation：兰德公司，美国著名智库，一家独立的、非营利性的研究和咨询服务机构

21. Odile：即黑天鹅奥黛尔，经典芭蕾舞剧《天鹅湖》中的角色

22. vacant [?ve?k?nt] adj. （表情等）茫然的;发呆的