John F. Nash Jr., a mathematician who shared a NobelPrize in 1994 for work that greatly extended the reach and power of moderneconomic theory and whose decades-long descent into severe mental illness andeventual recovery were the subject of a book and a 2001 film, both titled “ABeautiful Mind,” was killed, along with his wife, in a car crash on Saturday inNew Jersey. He was 86.

　　数学家约翰·纳什——1994年诺贝尔奖得主，其工作极大拓展了现代经济学理论的影响力和能量，他罹患严重精神疾病数十年并最终康复的故事是《美丽心灵》一书和2001年的同名电影的主题——周六在新泽西的车祸中与妻子一起丧生，终年86岁。

　　Dr. Nash and his wife, Alicia, 82, were in a taxi onthe New Jersey Turnpike in Monroe Township around 4:30 p.m. when the driverlost control while trying to pass another car and hit a guard rail and anothervehicle, said Sgt. Gregory Williams of the New Jersey State Police.

　　新泽西州警察表示，纳什和82岁的妻子艾丽西亚下午4:30在新泽西高速公路门罗镇路段出事，司机超车时市区控制，撞上护栏和另一辆汽车。

　　The couple were ejected from the cab and pronounceddead at the scene. The State Police said it was likely that they were notwearing seat belts. The taxi driver and the driver of the other car weretreated for non-life threatening injuries. No criminal charges have been filed.

　　纳什夫妇被甩出车舱，当场死亡。州警局表示他们可能没系安全带。出租车司机及另一个司机受伤，未危及生命。未提起刑事诉讼。

　　The Nashes were returning from Norway, where Dr. Nashand Louis Nirenberg, a mathematician from New York University, had received theAbel Prize from The Norwegian Academy of Science and Letters.

　　纳什夫妇刚从挪威回国，纳什和纽约大学的数学家Louis Nirenberg前往领取挪威科学与文学院办法的阿贝尔奖。

　　Dr. Nash was widely regarded as one of the greatmathematicians of the 20th century, known for the originality of his thinkingand for his fearlessness in wrestling down problems so difficult few othersdared tackle them. A one-sentence letter written in support of his applicationto Princeton’s doctoral program in math said simply, “This man is a genius.”

　　纳什被认为是20世纪最伟大的数学家之一，因其思想原创性及以少有人能及的勇气面对问题而闻名于世。其普林斯顿数学博士学位的一句话评语这样写：这个人是个天才。

　　“John’s remarkable achievements inspired generationsof mathematicians, economists and scientists,’’ the president of Princeton,Christopher L. Eisgruber, said on Sunday, “and the story of his life withAlicia moved millions of readers and moviegoers who marveled at their couragein the face of daunting challenges.”

　　“约翰的杰出成就激励了一代又一代数学家、经济学家和科学家。”普林斯顿校长C.L.Eisgruber周日说。“他和艾丽西亚的故事感动了数百万计读者和观众，他面临艰巨挑战时的勇气令人惊羡。

　　Russell Crowe, who portrayed Dr. Nash in “A BeautifulMind,” tweeted that he was “stunned,” by his death. “An amazing partnership,”he wrote. “Beautiful minds, beautiful hearts.”

　　在《美丽心灵》中饰演纳什的Russell Crowe发推文对其死亡表示“震惊”。“一段令人惊异的关系，美丽的心灵，美丽的灵魂。”

　　Dr. Nash’s theory of noncooperative games, publishedin 1950 and known as Nash equilibrium, provided a conceptually simple butpowerful mathematical tool for analyzing a wide range of competitivesituations, from corporate rivalries to legislative decision making. Dr. Nash’sapproach is now pervasive in economics and throughout the social sciences andis applied routinely in other fields, like evolutionary biology.

　　纳什博士1950年提出的非合作博弈理论(纳什平衡)

　　Harold W. Kuhn, an emeritus professor of mathematicsat Princeton and a longtime friend and colleague of Dr. Nash’s who died in2014, said, “I think honestly that there have been really not that many greatideas in the 20th century in economics and maybe, among the top 10, hisequilibrium would be among them.”

　　2014年过世的普林斯顿荣誉教授、纳什一直以来的朋友和同事Harold W. Kuhn说：“我真心地认为20世纪在经济学领域的伟大思想不多，纳什平衡是前十名的。”

　　A University of Chicago economist, Roger Myerson, wentfurther, comparing the impact of Nash equilibrium on economics “to that of thediscovery of the DNA double helix in the biological sciences.”

　　芝加哥大学经济学家Roger Myerson将纳什平衡对经济学的影响比作发现DNA双螺旋对生物科学的影响。

　　Dr. Nash also made contributions to pure mathematicsthat many mathematicians view as more significant than his Nobel-winning workon game theory, including solving an intractable problem in differentialgeometry derived from the work of the 19th century mathematician G.F.B.Riemann.

　　纳什对纯数学亦有贡献，许多数学家认为这些贡献比获得诺奖的博弈论更为重要，其中包括他解决了19世纪数学家G.F.B.黎曼的工作引申而来的微分几何难题。

　　His achievements were the more remarkable, colleaguessaid, for being contained in a handful of papers published bore he was 30.

　　同事表示，他三十岁之前发表的一些论文更显其成就之出色。

　　"Jane Austen wrote six novels," said BarryMazur, a professor of mathematics at Harvard who was a freshman at M.I.T. whenDr. Nash taught there. “I think Nash’s pure mathematical contributions are onthat level. Very, very few papers he wrote on different subjects, but the onesthat had impact had incredible impact.”

　　哈佛数学教授BarryMazur在麻省理工读大一时是纳什的学生，他说：“奥斯汀写了六部小说，我认为纳什的纯数学理论和奥斯汀一个级别。写的不多，主题不同，但个顶个地影响深远。”

　　Yet to a wider audience, Dr. Nash was probably bestknown for his life story, a tale of dazzling achievement, devastating loss andalmost miraculous redemption.

　　但对行外人而言，纳什的人生故事更为人熟知，其得其失均令人惊骇，其后还有奇迹般的救赎。

　　The narrative of Dr. Nash’s brilliant rise, the lostyears when his world dissolved in schizophrenia, his return to rationality andthe awarding of the Nobel, retold in a biography by Sylvia Nasar and in theOscar-winning film, starring Mr. Crowe and Jennifer Connelly as John and AliciaNash, captured the public mind and became a symbol of the destructive force ofmental illness and the stigma that often hounds those who suffer from it.

　　纳什的故事——起初光辉瞩目，继而在精神分裂症中崩颓，最后恢复理性获得诺奖——见于SylviaNasar的传记和Crowe及Jennifer Connelly饰演的奥斯卡获奖电影中。其经历震撼人心，成为精神疾病之毁灭力量的象征，让罹患精神疾病之人没齿难忘。

　　John Forbes Nash was born on June 13, 1928, inBluield, W. Va. His father, John Sr., was an electrical engineer. His mother,Margaret, was a schoolteacher.

　　约翰·福布斯·纳什生于1928年6月13日，西弗吉尼亚州的布鲁菲尔德。父亲老约翰·纳什是电气工程师，母亲玛格丽特是老师。

　　As a child, John Nash may have been a prodigy but hewas not a sterling student, Ms. Nasar noted in a 1994 article in The New YorkTimes. “He read constantly. He played chess. He whistled entire Bach melodies,”she wrote.

　　童年的纳什是个小天才，可算不上好学生，Nasar夫人1994年在纽约时报撰文称：“他经常读书，下棋，能把巴赫的旋律全哼下来。”

　　In high school, he stumbled across E.T. Bell’s book,“Men of Mathematics,” and soon demonstrated his own mathematical skill byindependently proving a classic Fermat theorem, an accomplishment he recalledin an autobiographical essay written for the Nobel committee.

　　他高中时偶然看到E.T.Bell的《数学大家》一书，很快就展示出其数学天分，他独立证明了经典的费马定理，这一成就在他给诺贝尔委员会写的自传文章中还提到。

　　Intending to become an engineer like his father, heentered Carnegie Mellon (then called Carnegie Institute of Technology). But hechafed at the regimented courses, and encouraged by professors who recognizedhis mathematical genius, he switched to mathematics.

　　立志于和父亲一样成为工程师，他考入卡耐基梅伦大学(当时叫卡耐基理工学院)。但他对刻板的课程很恼火，在教授的鼓励下转入数学系。

　　Receiving his bachelor’s and master’s degrees atCarnegie, he arrived at Princeton in 1948, a time of great expectations, whenAmerican children still dreamed of growing up to be physicists like Einstein ormathematicians like the brilliant, Hungarian-born polymath John von Neumann, bothof whom attended the afternoon teas at Fine Hall, the home of the mathdepartment.

　　在卡耐基获得学士和硕士学位后，他与1948年来到普林斯顿大学，那是一个激动人心的年代，美国孩子梦想着长大成为像爱因斯坦一样的物理学家或像出色的匈牙利大牛冯诺依曼一样的人，二人都在普林斯顿数学系的礼堂参加午后茶会。

　　John Nash, tall and good-looking, quickly became knownfor his intellectual arrogance, his odd habits — he paced the halls, walked offin the middle of conversations, whistled incessantly — and his fierce ambition,his colleagues have recalled.

　　纳什个头高挑，长得也帅气，恃才自傲，行为乖张，他在别人说话时踱出礼堂，哼着小调，他雄心勃勃，这些同事们都还记得。

　　He invented a game, known as Nash, that became anobsession in the Fine Hall common room. (The same game, invented independentlyin Denmark, was later sold by Parker Brothers as Hex.) He also took on aproblem lt unsolved by Dr. von Neumann and Oskar Morgenstern, the pioneers ofgame theory, in their now classic book, “Theory of Games and EconomicBehavior.”

　　他发明一种叫纳什的游戏，风靡礼堂的公共休息区，丹麦也独立发明了一样游戏，帕克兄弟将之出售获利，取名六连棋。他还着手解决冯诺依曼和摩根斯特恩在经典的《博弈论和经济行为》一书中没有解决的难题。

　　Dr. von Neumann and Dr. Morgenstern, an economist atPrinceton, addressed only so-called zero-sum games, in which one player’s gainis another’s loss. But most real world interactions are more complicated, whereplayers’ interests are not directly opposed, and there are opportunities formutual gain.

　　冯诺依曼和普林斯顿的经济学家摩根斯特恩只解决了所谓的零和游戏，即一家得益一家吃亏。可真实世界的交互更加复杂，玩家利益并不直接对立，有共同收益的机会。

　　Dr. Nash’s solution, contained in a 27-page doctoralthesis he wrote when he was 21, provided a way of analyzing how each playercould maximize his benits, assuming that the other players would also act tomaximize their self-interest.

　　纳什21岁撰写博士论文时用27页纸给出解决方案，他分析每个玩家会令其收益最大化，假设其他玩家也会最大化自我利益。

　　This deceptively simple extension of game theory pavedthe way for economic theory to be applied to a wide variety of other situationsbesides the marketplace.

　　对博弈论如此简单的引申为把经济学理论广泛用于市场外的各种情景中铺平了道路。

　　“It was a very natural discovery,” Dr. Kuhn said. “Avariety of people would have come to the same results at the same time, butJohn did it and he did it on his own.”

　　Kuhn说，“这是非常自然的发现，同时期许多人都能得到相同的结果，但约翰做了，用他自己的方式。”

　　After receiving his doctorate at Princeton, Dr. Nashserved as a consultant for the RAND Corporation and as an instructor at M.I.T.and still had a penchant for attacking problems that no one else could solve.

　　在普林斯顿获得博士学位后，纳什去兰德公司做咨询员，去麻省理工做讲师，仍然敢于挑战没人敢碰的问题。

　　On a dare, he developed an entirely original approachto a longstanding problem in differential geometry, showing that abstractgeometric spaces called Riemannian manifolds could be squished into arbitrarilysmall pieces of Euclidean space.

　　有一回，他开发了一套全然独创的方法，解决微分几何中由来已久的问题，表明被称为“黎曼流形”的抽象几何空间能被挤压为任意小的欧几里得空间。

　　As his career flourished and his reputation grew,however, Dr. Nash’s personal life became increasingly complex. A turbulentromance with a nurse in Boston, Eleanor Stier, resulted in the birth of a son,John David Stier, in 1953.

　　事业顺遂，名声鹊起，可纳什的个人生活日趋复杂，他和波士顿的护士Eleanor Stier恋爱并在1953年生了个儿子。

　　Dr. Nash also had a series of relationships with men,and while at RAND in the summer of 1954, he was arrested in a men’s bathroomfor indecent exposure, according to Ms. Nasar’s biography. And doubts about hisaccomplishments gnawed at him: two of mathematics’ highest honors, the PutnamCompetition and the Fields medal, had eluded him.

　　纳什的传记称，纳什还和几个男人保持关系，1954年在兰德公司工作时，他因在男浴室中露阴而被逮捕。对他成就的怀疑也令他痛苦：两个数学界的最高奖项，普特南竞赛奖和菲尔德奖都与他失之交臂。

　　In 1957, after two years of on-and-off courtship, hemarried Alicia Larde, an M.I.T. physics major from an aristocratic CentralAmerican family.

　　1957年，他与艾丽西亚在断断续续地恋爱两年后结婚。艾丽西亚毕业于麻省理工大学的物理学专业，来自中美洲的贵族家庭。

　　But early in 1959, with Alicia pregnant with theirson, John, Dr. Nash began to unravel. His brilliance turned malignant, leadinghim into a landscape of paranoia and delusion, and in April, he was hospitalizedat McLean Hospital, outside Boston, sharing the psychiatric ward with, amongothers, the poet Robert Lowell.

　　但1959年初，艾丽西亚怀着二人的儿子时，纳什出了问题，天才变成了疯子，陷入妄想和幻怔。当年4月，他去波士顿城外的McLean医院治疗，和诗人Robert Lowell一起住在精神病房里。

　　It was the first step of a steep decline. There weremore hospitalizations. He underwent electroshock therapy and fled for a whileto Europe, sending cryptic postcards to colleagues and family members.

　　这是厄运的开端。此后还有更多的入院治疗。他接受电击疗法，有一阵子逃到欧洲去，给同事和家人寄难解的明信片。

　　For many years he roamed the Princeton campus, alonely figure scribbling unintelligible formulas on the same blackboards inFine Hall where he had once demonstrated startling mathematical feats.

　　很多年来他都在普林斯顿大学闲逛，这个孤独的灵魂在礼堂的同一块黑板上写些难解的公式，他正是在这里展示过令人惊异的数学成就。

　　Though game theory was gaining in prominence, and hiswork cited ever more frequently and taught widely in economics courses aroundthe world, Dr. Nash had vanished from the professional world.

　　尽管博弈论大获成功，他的作品不断被引用，全世界的经济课都教授他的作品，但纳什自己从职业生涯中消失了。

　　“He hadn’t published a scientific paper since 1958,” Ms.Nasar wrote in the 1994 Times article. “He hadn’t held an academic post since1959. Many people had heard, incorrectly, that he had had a lobotomy. Others,mainly those outside of Princeton, simply assumed that he was dead.”

　　“1958年以后，他没有发表一篇科学论文。他1959年以后再也未获教职。许多人以为他做了脑叶切除，还有些不是普林斯顿的人直接以为他死了。”

　　Still, Dr. Nash was fortunate in having familymembers, colleagues and friends, in Princeton and elsewhere, who protected him,got him work, and in general helped him survive. Alicia Nash divorced him in1963, but continued to stand by him, taking him into her house to live in 1970.(The couple married a second time in 2001.)

　　还好纳什有家人、同事和朋友，有普林斯顿的，也有外面的，他们保护他，让他工作，帮他恢复。1963年，艾丽西亚和他离婚，但一直和他在一起，1970年让他到家里来住，二人2001年复婚。

　　By the early 1990s, when the Nobel committee beganinvestigating the possibility of awarding Dr. Nash its memorial prize ineconomics, his illness had quieted. He later said that he simply decided thathe was going to return to rationality. “I emerged from irrational thinking,ultimately, without medicine other than the natural hormonal changes of aging,”he wrote in an email to Dr. Kuhn in 1996.

　　上世纪九十年代初，诺贝尔委员会开始考虑授予纳什诺贝尔经济学奖，他的病情缓解了。后来他说他觉得自己正在恢复理性。“我最终非理性的思考中跳出来，没有用药，因为随着年老荷尔蒙水平变化了。”

　　Colleagues, including Dr. Kuhn, helped persuade the Nobelcommittee that Dr. Nash was well enough to accept the prize — he shared it withtwo economists, John C. Harsanyi of the University of California at Berkeley,and Reinhard Selten of the Rheinische Friedrich-Wilhelms University in Bonn,Germany.

　　包括Kuhn在内的同事们劝说诺贝尔学会，纳什的身体状况可以接受奖项，他最终和加州大学伯克利分校的John C. Harsanyi及德国波恩大学的Reinhard Selten共享诺奖。

　　The Nobel, the publicity that attended it, and themaking of the film were “a watershed in his life,” Dr. Kuhn said of Dr. Nash.“It changed him from a homeless unknown person who was wandering aroundPrinceton to a celebrity, and financially, it put him on a much better basis.”

　　“诺奖的光芒和好莱坞电影是他生命中的分水岭，这让他从在普林斯顿闲逛、无家可归的无名人士一下子成了名人，经济状况也大为改善。”

　　Dr. Nash continued to work, traveling and speaking atconferences and attempting, among other things, to formulate a new theory ofcooperative games. Friends described him as charming and diffident, a bitsocially awkward, a little quiet, with scant trace of the arrogance of hisyouth.

　　纳什继续工作和旅游，在会议上发言，更重要的是还提出了合作性博弈新理论。他的朋友说他迷人却有点害羞，待人腼腆安静，和年轻时的张狂全然不同。

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