約翰·納什：與瘋狂博弈的孤獨天才

他是天才，21歲就提出“納什均衡”，為博弈論研究帶來全新突破。他也是瘋子，曾因罹患精神分裂癥而被迫中止學術研究。他很不幸，剛成為數(shù)學界的耀眼新星便被病魔擊倒，人生陷入一片黑暗。他也很幸運，盡管瘋癲古怪，卻從未被家人和朋友拋棄，總能得到庇護和幫助。1994年10月，約翰·納什獲得諾貝爾經(jīng)濟學獎，這位一直在與病魔博弈的孤獨天才終于得到了應得的認可。2015年5月23日，納什因車禍離世，天才隕落，只留下世人的聲聲嘆息。

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.

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日揭曉年度諾貝爾經(jīng)濟學獎揭曉數(shù)周之前（編注：英文原文發(fā)表于1994年11月，納什獲得諾獎后不久），哈羅德·W·庫恩和小約翰·福布斯·納什這兩位數(shù)學家來到距普林斯頓大學不遠的梅多湖養(yǎng)老院，看望他們昔日的老師艾伯特·W·塔克。

納什離開房間后，庫恩又折回來告訴了塔克老師一個驚人的秘密：瑞典皇家科學院準備授予納什諾貝爾獎，以表彰1949年納什在塔克老師門下學習時所做的研究—這些研究后被證實對經(jīng)濟學有革命性的影響，而納什對這個消息還一無所知。

納什此番獲獎是一個奇跡。這不僅是因為納什—這位戰(zhàn)后時期的數(shù)學天才之一終于獲得了他應得的認可，也不僅是因為令他獲獎的是他在近半個世紀之前以21歲的弱冠之齡寫下的寥寥27頁的博士論文。

真正的奇跡在于，時年66歲的納什—高高的個子，頭發(fā)灰白，眼神憂郁，有著沉默寡言者的溫柔、沙啞的嗓音—依然康健，還能夠領獎。因為在30多年前，約翰·納什患上了妄想型精神分裂癥。

納什所患的可怕疾病在數(shù)學家和經(jīng)濟學家當中是個公開的秘密。1958年7月，納什被《財富》雜志評為美國“新數(shù)學”領域的耀眼新星，此后不久，疾病就摧毀了他的個人生活和職業(yè)生涯。自1958年起，他再未發(fā)表過學術論文。自1959年起，他再未擔任過學術職務。

他的人生一度充滿光明，前途似錦，后來卻變得如地獄般黑暗。他屢次被送進精神病院，經(jīng)歷失敗的治療，忍受著可怕的妄想。曾有一段時間，他在歐洲四處游蕩，還曾多次在母親和妹妹所居住的弗吉尼亞州的羅阿諾克住上一陣子。最終，他回到了普林斯頓—他曾作為一顆新星冉冉升起的地方。

起步階段：天資初露

20世紀50年代，納什曾在普林斯頓大學和麻省理工學院短暫任教，那里認識納什的人常用他的西弗吉尼亞出身來解釋他的不諳世事。不過，布盧菲爾德這個他從小長大的小鎮(zhèn)可算不上窮鄉(xiāng)僻壤。

納什的母親瑪格麗特是名拉丁文教師。他的父親老約翰是個溫文爾雅的電氣工程師。據(jù)納什的妹妹瑪莎·納什·萊格回憶，對老納什夫婦而言，沒有什么比監(jiān)督孩子們的教育更重要的了。小約翰是個神童，但不是全優(yōu)生。他總是在看書，會下國際象棋，能用口哨吹出整支巴赫的曲子。“約翰總是在尋找做事情的不同方法，”萊格夫人說，“他能找到跟老師不一樣的解題方法。”

1945年秋，納什在匹茲堡的卡內(nèi)基-梅隆大學（當時叫卡內(nèi)基技術學院）登記入學。正是在那里，納什第一次被貼上“天才”的標簽。他的數(shù)學教授有一天在課堂上稱他為“小高斯”。大一那年，納什從化學系轉(zhuǎn)到數(shù)學系，兩年后取得理學學士學位，并繼續(xù)攻讀理學碩士學位。

他讀研究生時的教授R.J.達芬回憶說，當時的納什是個個子高高、稍顯拘束的學生。有一天，納什來找他，跟他描述了一道難題，納什覺得自己解開了這道題。達芬教授不無驚愕地發(fā)現(xiàn)，納什獨立證明了布勞威爾的著名定理，而納什自己還不知情。達芬教授為納什所寫的推薦信只有一句話：“此人是個天才。”

引起轟動：博弈論及其他

1948年，納什獲得獎學金，進入普林斯頓大學攻讀博士學位。當時的普林斯頓可以說是數(shù)學界和科學界的中心。納什既渴望證明自己，又有些不善交際（這一點與那些曾經(jīng)入伍參戰(zhàn)的年齡較大的同學比起來尤為明顯）。他很快就成了才華橫溢的年輕學子中的一員，他們常在數(shù)學系大樓的公共休息室里展示自己超群的智慧。

同學們覺得納什性格孤僻，既聰明又古怪。他不是在公共休息室里滔滔不絕地演講，就是在踱步。他會沿著數(shù)學系大樓四邊形的走廊一圈圈地走，偶爾沖進一間空著的教室，在黑板上飛快地寫寫畫畫。“他一直是個不同尋常的人，”當年的本科生、現(xiàn)在的紐約州立大學石溪分校的數(shù)學家杰克·米爾諾說，“他常常想到什么就說什么。”

令納什贏得諾貝爾獎的論文是關于博弈論的，論文于他在普林斯頓求學的第二年寫就。博弈論的創(chuàng)始者是馮·諾依曼和普林斯頓大學一位名叫奧斯卡·莫根施特恩的經(jīng)濟學家。他們在1944年出版了著作《博弈論與經(jīng)濟行為》，首次嘗試從競爭關系中推導出邏輯和數(shù)學法則。

簡單地說，馮·諾依曼只是針對純粹的競爭提出了一個不錯的理論，在這種競爭中，一方的獲益就是另一方的損失。納什的研究則聚焦于也可能出現(xiàn)雙贏的競爭。他向人們表明，在各種不同的情況下這種競爭都存在穩(wěn)定的解決方案：考慮到其他參與博弈者的行為，參與博弈的各方都不會更占上風。如此一來，他就把博弈論從一種有趣的想法變成了一件強大的工具，經(jīng)濟學家們可以用它來分析從商業(yè)競爭到貿(mào)易談判的種種問題。“直到納什出現(xiàn)，博弈論才為經(jīng)濟學家們靈活運用。”麻省理工學院的諾貝爾經(jīng)濟學獎得主羅伯特·索羅說道。

1950年6月13日是納什22歲生日，當天他獲得了博士學位。他在普林斯頓做了一段時間的講師，又在冷戰(zhàn)時期的智庫蘭德公司擔任了一段時間的顧問。兩次短暫任職之后，納什于1951年前往麻省理工學院任教。

疾病來襲：“他完了”

20世紀50年代中期以前，納什在學術上成績斐然。和數(shù)學家們待膩了的時候，他會信步走到經(jīng)濟學系，同索羅及另一位諾貝爾獎得主保羅·薩繆爾森交談。

就是在這一時期，納什結識了他未來的妻子—麻省理工學院物理系的薩爾瓦多裔學生艾里西亞·拉德。艾里西亞是納什所授高等微積分課上的學生。她身材嬌小，舉止優(yōu)雅，有一雙烏黑的眼睛，就像《天鵝湖》中的奧黛爾一樣。“他非常非常帥，人很聰明，”納什夫人回憶道，“我對他的感覺有點像對英雄的崇拜。”他們于1957年結婚，那一年，納什從麻省理工的高等研究院請了一年的假。

待到納什夫婦回到麻省理工學院時，納什已經(jīng)取得了終身教職。納什夫人回到研究生院繼續(xù)學業(yè)，并在計算機中心做兼職工作。1958年秋，她懷上了他們的兒子約翰·查爾斯·馬丁·納什。“那是我人生中非常美好的一段時光。”她回憶說。

正當生活看起來如此甜蜜之時，約翰·納什病了。不出幾個月，在1959年的春天，30歲的納什被送進了麥克萊恩醫(yī)院，這是位于馬薩諸塞州貝爾蒙特的一家精神病院。

在入院前的幾個月里，納什完全變了個人。他說話時從一個話題跳到另一個話題。有時他講的有些課完全讓人不知所云。他一度拋下教書的工作，跑到羅阿諾克。他給許多公眾人物寫過內(nèi)容古怪的信。

“這讓人很難過，”當年不時遇見納什的加州大學洛杉磯分校的沙普利教授說，“完全沒法與他交談，甚至聽不懂他在說什么。”

總之，納什的妄想癥加重了，他無法再繼續(xù)工作。他辭去了麻省理工學院的教職，之后去了歐洲，在不同的城市游蕩。他擔心自己正在被監(jiān)視、追蹤，試圖放棄自己的美國公民身份。他的妻子和同事開始收到內(nèi)容怪異的明信片，其中許多都與數(shù)字有關。最終，納什夫婦分居了。納什搬到羅阿諾克和母親住在一起。

墜入深淵：20年的黑暗歲月

在隨后的20年里，納什的大部分時間是在醫(yī)院、羅阿諾克和普林斯頓度過的。他在普林斯頓待的時間越來越長。

1963年，納什夫人與他離婚，但最終同意讓他繼續(xù)住在家里。納什至少又住過三次院。納什夫人沒有再婚，依靠做計算機程序員的收入以及家人、朋友和同事們的一些接濟來養(yǎng)活前夫和兒子。

納什成了普林斯頓一個令人難過的游魂和神秘人物，成了數(shù)學系大樓的幽靈。“普林斯頓的每一個人看到他的樣子都知道是他，”20世紀70年代在普林斯頓讀研究生、如今是美國國家經(jīng)濟研究局經(jīng)濟學家的丹尼爾·R·芬伯格回憶道，“他衣服不太搭，看上去神情茫然，大多數(shù)時候都默不作聲。他經(jīng)常在圖書館讀書，或是在各個大樓間徘徊。”

艾里西亞·納什堅信，即使在不太能正常生活和工作的情況下，納什也應該住在家里，并待在普林斯頓的數(shù)學圈子里。瑪莎·萊格贊成她的決定。“待在普林斯頓對他有好處，”萊格夫人表示，“在普林斯頓那樣的地方，如果你舉止怪異，那表示你特別。而在羅阿諾克，你要是舉止怪異，那你就是另類。這里的人們可不知道他是誰。”

普林斯頓和麻省理工學院的一些前同事試著幫助納什，為他提供過一些研究工作。不過，通常納什沒法接受這些幫助。20世紀70年代，加州大學洛杉磯分校的沙普利教授成功地為納什爭取到了一項數(shù)學獎的現(xiàn)金獎勵。人們還以其他方式表達著善意，比如允許納什使用學校的計算機，或是在老朋友來學校時邀請他一起參加研討會。

病后回歸：病情終于緩解

然而，那些經(jīng)常與他保持聯(lián)系的人最終還是認為，他的病永遠不會好了。但是接下來就出現(xiàn)了庫恩教授所稱的“奇跡般的緩解”。據(jù)納什夫人和萊格夫人稱，就像在有些精神分裂癥患者身上所發(fā)生的那樣，這次不明原因的好轉(zhuǎn)不是任何藥物或療法的功效。“關鍵就是要平靜地生活。”納什夫人說。這次病情緩解最突出的標志或許就是納什又能研究數(shù)學了。

如今，納什是諾貝爾獎的獲得者。他獲獎這件事本身就是一種證明，不僅證明他戰(zhàn)勝了疾病，而且證明他在人們心中激發(fā)起了強烈的忠誠和崇敬之情。在納什患病的20多年里，博弈論蓬勃發(fā)展，在該領域的重要論文中，你很難發(fā)現(xiàn)有哪一篇論文是沒引用他的研究成果的。“納什發(fā)現(xiàn)的原理非常驚人，”另一位普林斯頓大學的數(shù)學家西蒙·柯晨表示，“納什是那種能讓人大吃一驚的人。”

1. Meadow Lakes：梅多湖養(yǎng)老院，美國一個持續(xù)照料退休社區(qū)（Continuing Care Retirement Community，簡稱CCRC），為老年人提供自理、介護、介助一體化的居住設施和服務。

2. raspy [?rɑ?spi] adj. 聲音嘶啞的;刺耳的

3. paranoid schizophrenia：妄想型精神分裂癥

4. single out：（從一群人中）選出，挑出

5. hellish [?hel??] adj. 地獄般的

6. stretch [stret?] n. 一段時間;一陣子

7. backwater [?b?k?w??t?（r）] n. 窮鄉(xiāng)僻壤;落后地區(qū)

8. prodigy [?pr?d?d?i] n. 奇才;天才;神童

9. Gauss：即約翰.卡爾.弗里德里希.高斯（1777～1855），德國著名數(shù)學家、物理學家、天文學家、大地測量學家，近代數(shù)學奠基者之一

10. 此處指布勞威爾不動點定理，是拓撲學里一個非常重要的不動點定理。

11. fellowship [?fel????p] n. （發(fā)給大學研究生的）獎學金

12. at once … and …：既……又……

13. gauche [ɡ???] adj. 不善交際的;笨拙的

14. pyrotechnics [?pa?r???tekn?ks] n. 出色的表現(xiàn);（本領的）炫示

15. Fine Hall：此處指普林斯頓大學的數(shù)學系大樓。

16. talk a blue streak：滔滔不絕地講話

17. quadrangular [kw??dr??ɡj?l?（r）] adj. 四邊形的

18. von Neumann：即約翰.馮.諾依曼（1903～1957），20世紀最重要的數(shù)學家之一，在現(xiàn)代計算機、博弈論和核武器等諸多領域頗有建樹，被稱為“計算機之父”和“博弈論之父”。

19. beguiling [b??ɡa?l??] adj. 迷人的

20. Rand Corporation：蘭德公司，美國著名智庫，一家獨立的、非營利性的研究和咨詢服務機構

21. Odile：即黑天鵝奧黛爾，經(jīng)典芭蕾舞劇《天鵝湖》中的角色

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