John F. Nash Jr., Math Genius Defined by a ‘Beautiful Mind,’ Dies at 86
By ERICA GOODE

John F. Nash Jr., a mathematician who shared a Nobel Prize in 1994 for work that greatly extended the reach and power of modern economic theory and whose long descent into severe mental illness and eventual recovery were the subject of a book and a film, both titled “A Beautiful Mind,” was killed, along with his wife, in a car crash on Saturday in New Jersey. He was 86.

Dr. Nash and his wife, Alicia, 82, were in a taxi on the New Jersey Turnpike in Monroe Township around 4:30 p.m. when the driver lost control while veering from the left lane to the right and hit a guardrail and another car, Sgt. Gregory Williams of the New Jersey State Police said.

The couple were ejected from the cab and pronounced dead at the scene. The State Police said it was likely that they were not wearing seatbelts. The taxi driver and the driver of the other car were treated for nonlife-threatening injuries. No criminal charges had been filed on Sunday.

The Nashes were returning home from the airport after a trip to Norway, where Dr. Nash and Louis Nirenberg, a mathematician from New York University, had received the Abel Prize from the Norwegian Academy of Science and Letters.

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

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

Russell Crowe, who portrayed Dr. Nash in “A Beautiful Mind,” posted on Twitter that he was “stunned” by the deaths. “An amazing partnership,” he wrote. “Beautiful minds, beautiful hearts.”

Dr. Nash’s theory of noncooperative games, published in 1950 and known as Nash equilibrium, provided a conceptually simple but powerful mathematical tool for analyzing a wide range of competitive situations, from corporate rivalries to legislative decision-making. Dr. Nash’s approach is now pervasive in economics and throughout the social sciences and is applied routinely in other fields, including evolutionary biology.

Harold W. Kuhn, an emeritus professor of mathematics at Princeton and a longtime friend and colleague of Dr. Nash’s who died in 2014, once said, “I think honestly that there have been really not that many great ideas in the 20th century in economics and maybe, among the top 10, his equilibrium would be among them.” A University of Chicago economist, Roger Myerson, went further, comparing the impact of the Nash equilibrium on economics “to that of the discovery of the DNA double helix in the biological sciences.”

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

His achievements were the more remarkable, colleagues said, for being contained in several papers published before he was 30.

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

Yet to a wider audience, Dr. Nash was probably best known for his life story, a tale of dazzling achievement, devastating loss and almost miraculous redemption. The narrative of Dr. Nash’s brilliant rise, the lost years when his world dissolved in schizophrenia, his return to rationality and the awarding of the Nobel, retold in a biography by Sylvia Nasar and in the Oscar-winning 2001 film, starring Mr. Crowe and Jennifer Connelly as John and Alicia Nash, captured the public mind and became a symbol of the destructive force of mental illness and the stigma that often hounds those who suffer from it.

Arrogant, Ambitious and Odd

John Forbes Nash was born on June 13, 1928, in Bluefield, W.Va. His father, John Sr., was an electrical engineer. His mother, Margaret, was a Latin teacher.

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

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

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

Receiving his bachelor’s and master’s degrees at Carnegie, he arrived at Princeton in 1948. It was a time of great expectations, when American children still dreamed of growing up to be physicists like Einstein or mathematicians like the brilliant Hungarian-born polymath John von Neumann, both of whom attended the afternoon teas at Fine Hall, the home of the math department.

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

He invented a game, known as Nash, that became an obsession in the Fine Hall common room. (The same game, invented independently in Denmark, was later sold by Parker Brothers as Hex.) He also took on a problem left unsolved by Dr. von Neumann and Oskar Morgenstern, the pioneers of game theory, in their now-classic book, “Theory of Games and Economic Behavior.”

Dr. von Neumann and Dr. Morgenstern, an economist at Princeton, addressed only so-called zero-sum games, in which one player’s gain is another’s loss. But most real-world interactions are more complicated; players’ interests are not directly opposed, and there are opportunities for mutual gain. Dr. Nash’s solution, contained in a 27-page doctoral thesis he wrote when he was 21, provided a way of analyzing how each player could maximize his benefits, assuming that the other players would also act to maximize their self-interest.

This deceptively simple extension of game theory paved the way for economic theory to be applied to an array of situations besides the marketplace.

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

Brilliance Turns Malignant

After receiving his doctorate at Princeton, Dr. Nash served as a consultant to 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. On a dare, he developed an entirely original approach to a longstanding problem in differential geometry, showing that abstract geometric spaces called Riemannian manifolds could be squished into arbitrarily small pieces of Euclidean space.

As his career flourished and his reputation grew, however, Dr. Nash’s personal life became increasingly complex. A turbulent romance in Boston with a nurse, Eleanor Stier, resulted in the birth of a son, John David Stier, in 1953. 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 bathroom for indecent exposure, according to Ms. Nasar’s biography. And doubts about his accomplishments gnawed at him: Two of mathematics’ highest honors, the Putnam Competition and the Fields Medal, had eluded him.

In 1957, after two years of on-and-off courtship, he married Alicia Larde, an M.I.T. physics major from an aristocratic Central American family and one of only 16 women in the class of 1955.

“He was very, very good looking, very intelligent,” Ms. Nash told Ms. Nasar. “It was a little bit of a hero-worship thing.”

But early in 1959, with his wife pregnant with their son, John, Dr. Nash began to unravel. His brilliance turned malignant, leading him into a landscape of paranoia and delusion, and in April he was hospitalized at McLean Hospital, outside Boston, sharing the psychiatric ward with, among others, the poet Robert Lowell.

It was the first step of a steep decline. There were more hospitalizations. Dr. Nash underwent electroshock therapy and fled for a while to Europe, sending cryptic postcards to colleagues and family members. For many years he roamed the Princeton campus, a lonely figure scribbling unintelligible formulas on the same blackboards in Fine Hall where he had once demonstrated startling mathematical feats.

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

“He hadn’t published a scientific paper since 1958,” Ms. Nasar wrote in the 1994 Times article. “He hadn’t held an academic post since 1959. Many people had heard, incorrectly, that he had had a lobotomy. Others, mainly those outside of Princeton, simply assumed that he was dead.”

Reaching a ‘Watershed’

Indeed, Dr. Myerson recalled in a telephone interview that one scholar who wrote to Dr. Nash in the 1980s to ask permission to reprint an article received the letter back with one sentence scrawled across it: “You may use my article as if I were dead.”

Still, Dr. Nash was fortunate in having family members, colleagues and friends, at Princeton and elsewhere, who protected him, got him work and in general helped him survive. Ms. Nash divorced him in 1963, but continued to stand by him, taking him into her house to live in 1970. (The couple married a second time in 2001.)

Ms. Nash supported her ex-husband and her son by working as a computer programmer, with some financial help from family, friends and colleagues.

By the early 1990s, when the Nobel committee began investigating the possibility of awarding Dr. Nash its memorial prize in economics, his illness had quieted. He later said that he simply decided that he 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.

Colleagues, including Dr. Kuhn, helped persuade the Nobel committee that Dr. Nash was well enough to accept the prize — he shared it with two economists, John C. Harsanyi of the University of California at Berkeley, and Reinhard Selten of the Rheinische Friedrich-Wilhelms University in Bonn, Germany — and they defended him when some questioned giving the prize to a man who had suffered from a serious mental disorder.

The Nobel, the publicity that attended it and the making 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 around Princeton to a celebrity, and financially, it put him on a much better basis.”

Dr. Nash is survived by two sons, John David Stier and John Charles Martin Nash, and a sister, Martha Nash Legg.

Dr. Nash continued to work, traveling and speaking at conferences and attempting, among other things, to formulate a new theory of cooperative games. Friends described him as charming and diffident, a bit socially awkward, a little quiet, with scant trace of the arrogance of his youth.

“You don’t find many mathematicians approaching things this way now, barehandedly attacking a problem,” the way Dr. Nash did, Dr. Mazur said.

「美麗境界」本尊…數學大師納許與妻車禍亡

故事被拍成電影「美麗境界」的諾貝爾經濟學獎得主、美國數學家納許（John Nash）與妻子艾莉西亞廿三日搭乘計程車發生車禍，雙雙身亡，納許享壽八十六歲，艾莉西亞八十二歲。

警方說，納許夫婦在下午四點半左右，搭計程車上新澤西州高速公路，司機企圖超車時失控，撞上護欄，當時夫婦倆沒有繫安全帶，被摔出車外，當場死亡。司機受傷送醫，沒有生命危險。

納許是普林斯頓大學和麻省理工學院的數學家，他研究衝突時決策的廿八頁賽局理論，1994年獲得諾貝爾經濟學獎。他的理論影響經濟、外交、政治、生物，以及所有有競爭和衝突的領域。

納許的心靈具有高度原創性，但也深受精神分裂症所苦。他獲得諾貝爾獎，改變了他的人生，在此之前，他沉寂了多年，數學界以為他死了。

人們透過電影「美麗境界」，看到他美麗的心靈。這部電影2002年獲得奧斯卡最佳影片。在片中飾演納許的演員羅素克洛獲知納許夫婦車禍喪生的消息後推文說：「了不起的夥伴、兩個美麗的心靈、兩顆美麗的心。」

納許和艾莉西亞．拉德1957年結婚，當時納許是數學界正在崛起的明星。婚後不久，納許的精神分裂症日益嚴重，電影「美麗境界」即以納許在數學上的突破、他為病魔所苦，及艾莉西亞幫助他克服疾病為主軸。

兩人在1962年離婚，但仍很親密，納許的病情在1980年代開始好轉，兩人在2001年第二度結婚。

本月稍早，納許獲頒被譽為數學界最高榮譽之一的挪威阿貝爾獎。

納許名滿天下 遭誣控反猶太

納許一生故事被拍成電影後，讓他成為知名度最高的諾貝爾獎得主之一。名滿天下謗亦隨之，各種流言八卦曾迫使他親自出面，澄清自己並非反猶太，也不是不敢出櫃的同性戀者。

納許1950年廿二歲時提出只有廿八頁的博士論文，讓他在四十四年後拿到1994年諾貝爾經濟學獎。剛獲獎時，媒體報導相當正面，多半著重在他如何克服精神分裂症，以及他理論的偉大。

不過，2001年他的故事改編成電影「美麗境界」後，許多人開始質疑電影過度美化他，指控他曾涉及反猶、和男子涉嫌猥褻等等八卦，迫使他當年主動出面澄清。

他表示，1967年的確曾寫過攻擊猶太人的信件，但他在1959年就罹患精神病，1970年才出院，或許曾在妄想狀態下說過可被解釋為反猶的話，但絕非本意。他在病發前的幾個最好的朋友，都是猶太人。

有些支持同性戀者權益的人說，他們對「美麗境界」片中未談到納許1954年曾在一處公共廁所因猥褻暴露被捕，他們認為此事即為納許可能是同性戀者的證據。

納許否認自己是同性戀者，但他不願多說，僅說：「我對此最好三緘其口。」納許的妻子艾莉西亞也說，她非常確定丈夫不是同性戀者，艾莉西亞說：「我廿歲就認識他，此事並非事實。」

不過，他雖然和夫人艾莉西亞鶼鰈情深，卻曾在兩人婚前，對一個懷了他孩子的護士始亂終棄。當時是1952年，納許剛獲聘為麻省理工學院講師，他生病時結識護士伊蓮諾．史迪爾，對方懷了他的孩子，納許卻拋棄她，據說納許認為對方的身分配不上他。這一段故事，也沒有在電影「美麗境界」中呈現。

獨特天才 納許生活也「賽局化」

美國數學家納許因電影「美麗境界」而聲名大噪，很多人知道他克服精神病拿到諾貝爾經濟學獎的故事，對他最主要的學術成就「賽局理論」卻一無所知。其實，這位被眾人認為行為怪異的天才，得獎原因竟是他對人類行為的洞察。

賽局理論是匈牙利數理天才馮諾曼在1928年率先提出。馮諾曼觀察撲克牌賭局，成功的將人類競爭行為以邏輯和數理規則加以分析。在這類行為中，參加競爭的各方各有不同的目標或利益，因此必須考慮對手的各種可能行動方案，再找出對自己最有利或最合理的方案。傳統的賽局理論，就是研究競爭各方是否存在著最合理的行為方案，以及如何找到這個合理的行為方案的數學理論和方法。

納許絕對信仰理性和思考的力量，他研究學問的態度就是孤獨的研讀前人著作加上天馬行空的創意思考。他的偶像都是一些著名的孤獨思想家和「超人」，如尼采與牛頓。

他沉迷於電腦和科幻小說，而且想把生活完全化為數學規則，用賽局理論來分析某項決策的優劣，完全去除情緒、風俗、傳統的影響，甚至連在哪家銀行存錢、在哪裡工作、要不要結婚都加以「賽局化」。

原文參照：
http://www.nytimes.com/2015/05/25/science/john-nash-a-beautiful-mind-subject-and-nobel-winner-dies-at-86.html

紐約時報中文版翻譯：
http://cn.nytimes.com/obits/20150525/c25nash/zh-hant/

延伸閱讀：
http://www.nytimes.com/2015/05/25/science/explaining-a-cornerstone-of-game-theory-john-nashs-equilibrium.html
http://www.nytimes.com/interactive/2015/05/25/science/johnnashquotes.html

2015-05-25．聯合報．A13．國際．編譯田思怡