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

May 25, 2015 · 307 comments
Progressive Christian (Lawrenceville, N.J.)
A few here have written of the terrible irony of such a brilliant man making such a stupid decision - not to wear a seat belt in a vehicle driven at high speed by someone who was a complete stranger to him. How many of us would never think of driving our own car without a seat belt and yet blithely neglect the simple act of buckling up when we're in a taxi or limo? Now add the incentive that the typical livery driver has to speed or cut safety corners to get to the next fare and logic tells us that seat belts are even more important in a taxi than in our own vehicle. A beautiful mind indeed, but a foolish one as well, resulting in needless suffering and death. We can add John and Alicia Nash to the list of otherwise smart and/or successful people who were either killed or seriously maimed in this manner - Bob Simon, Jon Corzine, Miracle on Ice coach Herb Brooks, and perhaps comedian Tracy Morgan as well (though the facts in that case are in dispute). The lesson here is that neither brains, money, political power nor celebrity can protect someone from failure to use a simple seat belt. Take heed. Your life may depend upon it.
Barbara Lakota (New York, NY)
I don't understand how this accident happened. I think the taxi driver must be an idiot. Unspeakably sad. . . .
Tony N (Bloomfield Hills, MI)
Summer Michigan State 1972, Game Theory was only touched on at the end of an accelerated term but I will always remember the feeling of completion from the Nash Equilibrium vs. the historical Tableau, Cournot and the zero sum theoretical startup from von Neuman. The flash of light from all the potential applications was all the chatter in our study group all trying to rush the material to get quick credit and half a summer vacation. As a nation we are deluded by the mindless worship of equality. All men are not created equal. We have no system to protect and preserve human geniuses. Why did we give responsibility for Prof Nash and his wife airport transportation over to a random public taxi driver? The loss for humanity cannot be measured.
My hope is the realization of the value to mankind from world renown contributors will jolt institutions and family to create systems of protection and preservation.
God bless you Prof and Mrs. Nash.
Phanindra (Nepal)
My wife at first asked with me to read a Nobel " A beautiful mind", since my English is not sophisticated, I red it with her with difficulty. Then I loved the genius figure Dr Nash. Later I got a move on him, A beautiful mind. Since then, even though I am the anatomist, John F Nash is my great source of inspiration. I and my wife Chacchu miss him a lot. At this moment of great loss of genius figure from this earth, we pray with the god for the peacefulness to the departed soul.
Montani (WV)
My deepest sympathy to the family of Dr. Nash. He was an inspiration to millions, but especially West Virginian young people. Because of Dr. Nash and also the "Rocket Boys" of West Virginia the casting of West Virginians as hicks and rednecks by elitists is much more difficult.
Molly (Massachusetts)
Why no obituary for his wife, Alicia who died with him and arguably was the one person in his life who fought his mental illness with him side by side? Loving someone with severe mental illness is so isolating and demoralizing. A thoughtful recap of her life and struggles could be beneficial to so many and it seems only fair since they died together.
archer717 (Portland, OR)
I too found E. T. Bells's "Men of Mathematics" endessly fascinating, though, truth to tell, there really isn't much mathematics in it. Bell assumed you were already acquainted with the work of these men. And yes, they wee all men; he mentions Olga Kowalevski, one of Weierstrass's students, only in passing and he ignores the much more important Emma Noether altogether.

But he would have done better had he first stumbled upon Courant and Robbins "What is Mathematics?", still (it was first published in 1941) the best introduction to the subject. But I'm sure Nash eventually did find it, as did virtually every mathematician of his - and our - time.

i hope Paul Krugman will devote his next column to a discussion of Nash's theory and its relevance to today's economic problems.
Robert (Twin Cities, MN)
Actually, Bell devoted a fair amount of space to the relationship between Gauss and Sophie Germain (who had originally written to Gauss pretending to be a man). However, I agree there are many problems with the book, including the omission of Emmy (not "Emma") Noether who, with assistance from Hilbert, became one of the great 20th century mathematicians--even though she died in her prime.
CJ (San Diego, CA)
Rest in peace. May his mind finally reach the equilibrium that he has long sought.
Observer from the North (Montreal, Canada)
An astonishing accomplishment of a mind with clearly backward neurone wiring but a central push for equilibrium.
Harriet (Albany)
Maybe it is time to look at the taxi industry. In NYC each cab only has $100,000. inaurance covergae. Many are driven by people from third world countries. How long have they been driving before they are unleashed on NYC traffic and pedestrians.
Kathryn Tominey (Benton City, Wa)
Cabs do not have seat belts - not required. Driver was speeding and driving recklessly. What a tragedy.
Dr. Pablo Guerez Tricarico (Madrid, Spain.)
John Nash has left us. A great example of perseverance and a reference model for many people who consider ourselves aspiring intellectuals, scientists and non-scientists, among whom I am. He made a brief foray into game theory earned him the Nobel Prize in economics for his research in this area of ​​knowledge, with its contribution of Nash equilibrium. He strongly influenced many specialists involved in games theory's investigations, but his research transcended beyond pure mathematical field, a field in which he felt most comfortable and where he received his greatest recognition from the scientific community for his research on developments partial derivatives. On the human level, his contributions helped to develop the foundations of a new cooperative economy, not based on profit, and the appreciation of the importance of the non-zero-sum games, ie, cooperative games. A man of extraordinary intellectual and moral stature. In his weakness he lays his strength, locked in the mysteries of the human brain and mind. His awesome personality reflected as never the cross of the social stigma of a different brain function pathologized by society and the glory of scientific recognition, this really objective, beyond any contingency and imperfect science emerging regarding the "social sciences", like psychology or economy, that seek to establish a Theorie of the whole man. Absurd. But absurdity does not exist in the pure mind of John Nash.
Richard (Albertson, NY)
A couple of observations.
Though being named a Putnam Fellow is certainly an attainment of note, there are certainly more prestigious honors.
* Which brings us to the Fields. *
We should begin by noting that, during most of the time Nash was eligible to receive it, only two medals were awarded: the maximum number of medals awardable was raised to four in 1966, his last Congress of eligibility. [It should also be noted that the Fields Medal Class of 1966 was spectacular even by the standards of the Fields: Atiyah, Grothendieck, Smale and Cohen (An almost * comically * august assemblage.).]
The award hit rock bottom in 1974. Though four medals * could * have been awarded, only two were -- to Bombieri and Mumford [N.B. No one has EVER questioned the deservingness of Bombieri and Mumford: both are giants (though some might hold Mumford to be slightly gianter).]. -- Arguably no fewer than * five * other mathematicians (All in their last Congress of eligibility.) would have been worthy recipients: Barry Mazur*, Robert Langlands ( * The Langlands Program * : enough said.), Yuri Manin (A buncha stuff.), Vladimir Arnold (The "A" in "KAM".), and John Horton Conway (The perpetrator of much yummy mischief.).

* Affectionately known as "Don Mazur" (Cf. "Don Corleone".) -- on account of his status as the Godfather of number theory -- he is the source of the much-quoted crack, "I'm gonna make him a conjecture he can't refute.".
Anon Comment (UWS)
Thank you for sharing the information.
Lou C. (Baltimore)
A truly inspired and inspiring story concluding. As we are thankful for his mind, its strength, beauty, and resilience, and as we are thankful for his work and all that has flowed from it, let's resolve to hold lives like both of theirs up as heroic. Let's reserve our attention and awe for people like them, rather than the celebrities, athletes, and other one trick ponies who seem to absorb our fascination. Let's celebrate the love they shared and honor the friends and colleagues who never deserted them. Let's be more like them.

Godspeed to the Nashes.
Richard (Albertson, NY)
A man -- once subsumed in a haunting -- who would eventually harrow it: something * very * few ever do.
I saw him but once, and (I believe) told him I admired him for dealing with some hard things -- sadly, I am not sure he heard me (He was clearly hard of hearing by that time.).
May King (Toronto, Canada)
I am not keen about math genius, but humanity genius. I do not know or understand the REASON that economy of 21st century collapsed globally while audience greatly praises Dr. Nash's theory of GAME CHANGER.

I am sorry to acknowledge Dr. Nash and his brilliant, devoted wife passed away tragically. My deepest sympathy is with families'members of both Dr. Nash and his wife Alicia. May God bless both of their souls to Heaven.
Dalana Dailey (Lakewood, WA)
A brilliant man overcomes a debilitating mental illness and is awarded a Nobel prize. He marries an unbelievably dedicated woman and their love endures through the decades. Both in their eighties, they leave this world together.

Call me callous but I do not think this is a tragedy. This is the best we can aspire to. This is a beautiful life.
Moses (Pueblo, CO)
There was a very well done video posted on the website of Hindustan Times on Professor Nash and his Nash Equilibrium. It also included video of his wife. To go through what they went through and then, then returning after winning a prize overseas, die at the hands of a crazy speeding taxidriver on the NJ Turnpike is the ultimate tragedy.
Lynne (New York)
I know they were elderly, but this is the same kind of thing that caused CBS 60 Minutes Bob Simon's death. Careless & reckless driving by people who really don't have a right to a drivers license. Car Services & Airport Taxi's are very dangerous. I'm sure there are more of these kinds of tragedies that we are not aware of.
Henry Bogle (Detroit)
Why did it take winning a Nobel to rescue this mentally ill man from being virtually homeless on the campus where he had taught? Perhaps ironically, Dr. Nash fell victim to the same zero-sum game mentality and culture he was trying to change. RIP
Steve Singer (Chicago)
Most homeless people are mentally ill. They're unable to function in society, at any level; why they can't earn a decent living; why they're homeless.

Most of the mentally ill homeless living on the street are ignored by the rest of us and they are persecuted by our legal system. In that sense, Prof. Nash was lucky.

Most mentally ill homeless die on the streets in penury, shunned, ignored and in disgrace.
Rohit (New York)
Two people who should be mentioned at this moment are Shizuo Kakutani and L.E.J. Brouwer. Nash's first PNAS proof of the existence of a Nash equilibrium used Kakutani's fixed point theorem. His second proof used the Brouwer fixed point theorem.

These two men should also be honored, and remembered.
Shawn Gilronan (Hinckley)
I started following the career and life of John Nash after the movie with Russell Crowe debuted. He truly was a pioneer and visionary in the field of mathematics. Generations to come will be studying his works and publications. He will be missed.
Justus99 (Raleigh, NC)
What a terrible, terrible loss. John and Alicia Nash served as inspiring role models in the mental health community. He will be remembered not only for his genius, but his persistence in continuing to contribute to mathematics when he could have succumbed to despair. None of the medicines available today to help people recover from schizophrenia -- the atypical antipsychotics - existed when he became ill. Alicia Nash will be remembered for her enduring love. She sacrificed what could have been a brilliant career in academia to protect and support her family. My sincerest condolences to Dr. Nash's sons. Your parents had such a difficult life, though ultimately triumphant, that I am sorry that you had to lose them in such a tragic way. But they were both heroes and will not be forgotten.
stonecutter (Broward County, FL)
Seems supremely ironic that a man of such monumental accomplishments in his field, accomplishments that elevated so many other fields of human endeavor, and his amazingly devoted wife would end up dying in a supremely mundane car accident on the NJ Turnpike, in the backseat of a taxi no less, after enduring so many years of extreme mental challenges and then struggling back to "rationality". An "ignominious" death only begins to describe it. He undoubtedly recovered his sanity with the same intense will and focus that engendered his mathematical genius. RIP.
danleywolfe (Ohio)
Great obituary - essay on a very special person. The title of Sylvia Nassar's outstanding book and the wonderful movie with Russell Crowe based on the book is proper tribute to the great man .. "A Beautiful Mind."
Mac Zon (London UK)
The tragedy in reading this article is that two not one person died in this tragic accident but not one honorable word was mentioned about his wife that sacrificed her well being and happiness to attend to this lost soul for many, many years. Dr Nash was a great man but without his wife's endless support, it would have been lesser.
anthony weishar (Fairview Park, OH)
The best way to honor Nash's passing is by changing our treatment of and attitudes toward the mentally ill. There are more John Nash's waiting to be discovered. We have to redirect the focus from making them normal to seeing their skills and unique talents. They possess unique logic and sensory abilities far beyond any advanced learning or current technology. But they remain isolated.

It was a blessing that John Nash was free to explore the powers of his mind. Honor his passing by dedicating more effort to understand and communicate with our mentally ill. They are not dumb, they just communicate differently.
JM (CT)
Can somebody please tell me where Alicia Larde Nash's obituary is?
JM (CT)
I am shocked that the New York Times does not seem to think that Alicia Nash merits her own obituary. I was going to hit "subscribe" today because they are running a half off subscription series; however, because I cannot find her obituary on their site, I see no reason to support an institution that doesn't recognize Alicia Nash's critical role in her husband's work and life. In her day, there wasn't much opportunity for a woman in math and science. As the NYT reports in their obituary of her husband, she was "one of only 16 women in the class of 1955" at MIT. Does the NYT believe that women such as Alicia Nash should be ignored? Through no fault of their own, but due to the patriarchal system in the USA, women such as she had extremely few routes to their own professional achievements. Were it not for Alicia Larde Nash, there'd be no celebrating of John Nash's achievements and arguably no NYT obituary.
DW (Philly)
Oh, give it a rest. I am sure they will publish her obituary. He was the famous person, not her, so no doubt they had a mostly-prewritten obit for him, but hers might take a little longer. Also, for a couple to die together is rare. Normally you can get details to flesh out an obituary from the surviving spouse, and collect facts on the survivor at that time, for later use. The Times cannot foresee the slim odds the couple would die within 5 minutes of each other, and it would have been a little unseemly to go to him asking for details for her obituary while she was alive.

Believe me, I am an ancient, bra-burning, card carrying feminist. But this is ridiculous.
Country Mouse (Westchester)
Thank you for writing this. I couldn't agree more. Additionally, she had to be a caregiver for her husband and her child - which I'm sure limited her own career potential. There are a lot of women and mothers today in this very situation. And while I want to be respectful to Nash - I agree the absence of her own obituary is a reflection of the ignorance that continues in our country today.
me (world)
Why are you so sure, DW? I would wager that NYT will NOT publish her obit, for the very reasons you allude to: he was the famous one, and the facts in his obit about her are deemed sufficient. But they aren't.
Tom (Connecticut)
It was unfortunate that his psychological "condition" was so sensationalized by the movie; frankly he deserved better than to be used by the profiteers. And many questions remain on the advent of crippling mental conditions and all their causes, and treatments. Extremes in any case undermine the delicate balance of the mind and treatments over the years in many cases have done more harm than good. And the rates of psych drugs now being pushed on Western society, will one day be looked at as a wrong-headed solution to failures to be "normal". Someone with as unnatural lifestyle as most intellectuals I have known with lousy nutrition and diets, what do you expect when they try to maintain their genius with the huge physical resources required?
kathleen cairns (san luis obispo)
Alicia Nash is the hero of this story--and of John Nash's life--and yet she rates only a few lines, scattered here and there in this excellent obit. Of course John Nash was a towering genius, but he could not have achieved nearly as much without the foundation she provided. Accomplishments come in many shades, not just academic and theoretical brilliance.
DW (Philly)
"she rates only a few lines, scattered here and there"

That's because it's not her obituary! Good grief.
JM (CT)
I am shocked that the New York Times does not seem to think that Alicia Nash merits her own obituary. I was going to hit "subscribe" today because they are running a half off subscription series; however, because I cannot find her obituary on their site, I see no reason to support an institution that can't recognize Alicia Nash's critical role in her husband's work and life. In her day, there wasn't much opportunity for a woman of science. As the NYT reports in their obituary of her husband, she was "one of only 16 women in the class of 1955" at MIT. Does the NYT believe that women such as Alicia Nash should be ignored? Through no fault of their own, but due to the patriarchal system in the USA, women such as she had extremely few routes to their own achievements. Were it not for Alicia Larde Nash, there'd be no celebrating of John Nash's achievements and arguably no NYT obituary.
JM (CT)
Yet where is her obituary?
Trish (Canada)
If you have seen the movie, "A Beautiful Mind", much of it is nonsense and greatly alters the truth and realities of his marriage.

Unless Ms. Nassar was writing fiction in her biography, one must go to this book for the real biography.

He was a brilliant man and a loss to the academic world. I'm sure that his wife was devoted to him but the movie was to a great degree fiction.

Read the book.
Anon Comment (UWS)
The book was very, very well-written. I have re-read it many times.
Steve Singer (Chicago)
Movies are metaphors. They must be. The structural demands of the art form act like a straight-jacket. Deviate too far from them, experiment too much, you risk losing the audience.

Time and space must be condensed to a degree bordering on nonsensical. States of mind, being invisible, cannot be depicted onscreen, merely suggested. Subjects, objects, protagonists and antagonists are mere vectors pushing the audience into some otherwise unreachable subtextual, subliminal place in their own minds -- if the movie "works", as is said.

Most don't.

But "A Beautiful Mind" did work, after-a-fashion.
FreeSpirit (Blowin' In The Wind)
Quite a coincidence that this tragic piece follows an article about Uber's expansion to airports. Is there a connection?
Karen (New Jersey)
Rest in peace, Dr Nash
Ed Bloom (Columbia, SC)
A lot of commenters are calling the manner of his death a tragedy. I agree only in the sense that all deaths are tragic. But I was heartened by the fact that he didn't go in a fit of madness and/or by his own hand. That was the way I assumed he would go. Instead, after a long life, he died in an accident with the remarkable women who stood by him by his side.

Rest in peace, John Nash.
al (medford)
A senseless, un-nessesary avoidable accident by a man who will walk home and go on with his useless American dream. It's just a real shame the Nash's were killed by ineptness.
Jim (WI)
This accident was no accident. Nash and his wife were taken out by assassins hired by Hitler to takeout the code breaker.....
ZoetMB (New York)
I think you're confusing John Nash and Alan Turing. Turing died in 1954.
lloyd (franklin)
The application of Dr. Nash' genius goes way beyond mere abstraction. His equilibrium theory shapes the world. Its probable that Bush senior left Hussein of Iraq in power because his regime kept equilibrium in the middle east. When the next Bush believed that Hussein had weapons of mass destruction, our equilibrium equations indicated that equilibrium in the region was about to end and the younger Bush (perhaps for other reasons) attacked. We are now seeing the affect of the Bush jr. misapplication of the equilibrium theory as evidenced by the disequilibrium in the middle east. The equilibrium theory was also widely used during the cold war.
al (medford)
Anyone taking a taxi these days are allowing anyone from anywhere to put their lives at risk. This taxi driver was on the job for only 2 weeks! How do you loose control on the Turnpike? distracted by his phone? Hopefully, he will be charged for manslaughter. Lack of respect for life, including his own.
Hal (Miami)
It is heartening and heartwarming to read about the life of a person as unique as Dr. Nash.

In the modern world, surrounded daily by overwhelming media and political distortion of scientific facts and discoveries, we need to be enlightened by the genius of pure thought such as he brought.

The world needs more thinkers like Dr. Nash.
Occupy Government (Oakland)
we do have such thinkers... panhandling and sleeping under bridges. we lack the wherewithal to project society's interest in helping them succeed.
philip mitchell (ridgefield,ct)
rip, emperor of antartica!! descansen en paz, gente marvillosa.
Sid (Kansas)
His singular and stunning achievements as a genius without peer are all the more astonishing considered in the context of his struggle with insanity. That he could walk out of that jungle is itself a wondrous achievement. Clearly, his emotional passions created another personal crisis as well yet he surmounted them and gained the love and support of a wife with immense courage and commitment. Their lives are to be celebrated together for without her he might have been lost without recourse or remedy. God love them both for they had a bond that saved his life. She might be considered by some a saint for her courage and commitment. There are few love stories as compelling and beautiful as theirs.
Mario Cobucci Junior (São Paulo, Brasil)
Gone is a genius, like Alan Turing marked as anyone his passage through life.
Both, just let us never forgotten lessons, coincidentally both endured internal conflict and perhaps also why offset in science.

John Nash am immensely grateful to his theory of the games that both studied at graduation as the MBA. May God bless you and be the guardian of your soul.
ERP (Bellows Fals, VT)
I think that it is disrespectful to assert that a person is "defined by" a movie or a book about him.
DJS (New York)
It’s chilling that the Nobel Committee had to be convinced that a mentally ill individual should be allowed the award a Nobel prize. Does the Nobel Committee need convincing when it comes to awarding a Nobel Prize to individuals who happen to be suffering from Cancer or other illnesses that are not “mental illnesses”?!
Steve (New York)
Considering that the Nobel Prize in literature has gone to many alcoholics, obviously the Nobel committee on this prize hasn't been bothered by their suffering mental illness.
Fred (New York)
The Nobel Committee that awards the prize for literature is separate and distinct from the prize committee for the "Sweden's Riksbank Prize in Economic Sciences in Memory of Alfred Nobel".
Ralph (NSLI)
Always wear your seatbelt. Simple lesson, even for a genius.
Mac Zon (London UK)
Good point but did you ever slip or fall and then wish you had taken more care to avoid the accident?
blgreenie (New Jersey)
What is most moving to me about these comments, more than testimony to Prof. Nash's intellectual contributions, is the hope and strength gained from him by those and their families, struggling with mental illness, who learned about the success in his own struggle.
Bill Wolfe (Bordentown, NJ)
Nash's work made some dark and paranoid assumptions about human nature.

Nash’s assumptions on human nature, reflected in game theory, were twisted: to Nash, humans were driven exclusively by ruthless and selfish individual self interest – a world where empathy, altruism, solidarity, the social contract, collective action, and cooperation did not exist.

These ideas poisoned other fields, leading to the madness of strategic nuclear deterrence, free market economics, public choice theory, and libertarian politics.

In a supreme irony, apparently Nash was not wearing a seat belt. The irony does not flow from his mathematician’s misperception of quantitative risk.

Seat belts were a government regulatory mandate – in contrast, Nash’s ideas reinforced radical free market economic theories like those of Freidrich Hayek, who viewed such government intervention – before the slogan “command and control regulation” had been coined – as a step along The Road To Serfdom.
amy (St. Louis MO)
Based on descriptions of his mental health issues and idiosyncratic behavior I would guess that Nash had Asperger's syndrome which is a form of Autism. Highly intelligent but unable to comprehend the basic social concepts that you mentioned: empathy, altuism, solidarity etc.
Marilyn Wright (Chicago)
Looking at the world today, I think Nash's assumptions about human nature were spot on.
Gwbear (Florida)
A tragic, and violently sudden ending. The fact that they were both ejected from the vehicle tells you all you need to know about this terrible event.

People should wear seatbelts... and taxi and limo drivers should take far more care.
PARIS SVORONOS (BAYSIDE NY)
What a loss. He was not only a genius- by overcoming all odds he became the role model to so many struggling people. May God rest him in peace. And may He also bless his loyal wife who was his walking cane during his difficult times.
John (Nesquehoning, PA)
I find John Nash's story compelling and an inspiration to all that have suffered with mental illness. He was one of the true geniuses of the 20th century. As much as we morn the loss of John Nash we should also morn the loss of his wife Alicia. I believe without her devotion and determination to stand by her man John Nash would have faded into obscurity. I wonder how many people today would show such devotion? My feeling is very few. My you rest in peace John and Alicia Nash.
FHS (Miami)
Picasso said something along the lines of always wanting to keep painting like a child. Nash did most of his best work as a young man. Why are great insights largely reserved to the young? That goes for great artists, mathematicians and scientists.
Don (Pittsburgh)
The belief that precocity and genius are inextricably related (That) ain't necessarily so". For a brief review take a look at the New Yorker article by Malcolm Gladwell, published in the October 20 2008 article: "Late bloomers. Why do we equate genius with precocity?"
Ancient (Western NY)
Most accomplished musicians would disagree with your theory, and Dave Brubeck would laugh at it if he were alive.
Mac Zon (London UK)
Because your brain is well cooked by the age of 30 :-)
Richard Luettgen (New Jersey)
Does this mean that Jennifer Connelly is free?

Sorry. Couldn't resist that, but Prof. Nash, for all his sufferings, lived quite a life and was given the intellectual assets to have made it more impactful to humanity than almost all of us could ever know ourselves.

We all will die, but very few of us will leave behind the wealth of contribution that he did.
Gareth Andrews (New York)
He proved Fermat's theorem? Really? Then why did he not win the prize for solving it, the prize that was offered a number of years ago?

Something's wrong somewhere....either in the facts of what happened or in the reporting.
Gary K (Mansfield, OH)
The theorem he proved by himself was Fermat's "little theorem," which says that if x is any integer and p is a prime then x^p minus x is divisible by p. Today this will be encountered by any math major in their first course in abstract algebra. Fermat really did prove it. The more famous statement perhaps should be called Fermat's conjecture, since it wasn't proved until 20 years ago by Andrew Wiles.
xbnv (NY)
In elementary number theory there is a basic result called "Fermat's Little Theorem" (having nothing to do with the more famous "Last Theorem"). That is the result to which the article is referring. (The "Little Theorem" says that if p is prime and x is an integer then x^p - x is divisible by p; see Wikipedia for more on this result.)
Chris Judge (Bloomington IN)
According to Wikipedia, Fermat did not write down a proof of the "lttle theorem'. Apparently the firs proofs were due to Leibniz and Euler.
Brian (Eastern Shore Maryland)
I was a seminarian at Princeton Seminary and then a graduate student at Princeton in the 70's and taught there for five years until 1985. I never knew Mr Nash. I was in the humanities, though I would see him from time to time. There was a magnetic presence about him and a kindness that was comforting. Only later did I know his story. His greatness preceded was great but with his story he was a giant.
Stuart Wilder (Doylestown, PA)
On so many levels his life is an inspiring story if a struggle against adversity and for excellence.
S. Mckee (Muncie Indiana)
In the photo, he is making Pi with his fingers: 3-1-4.
Anon Comment (UWS)
Thanks for pointing that out.
David (New York)
The film was certainly what made him famous among the general public, but it definitely did not define him. His momentous contributions to science did.
srwdm (Boston)
A thought to consider:

IF John Nash had NOT recovered from the debilitating mental illness—a far more likely scenario in cases like his . . .

THEN the remarkable efforts of his wife would be just as commendable, even more so . . .

BUT the movie would never have been made AND this obituary would most likely be a footnote.
Vishwas Nimbalkar (India)
It was very terrible to hear that he is no more. A Genius in his own sense. Prof. Nash and his ideas of equilibrium may have influenced the Modern Economic Theory, but the struggle of his life, his fight against the Schizophrenia is an inspiration of millions around the world.
When millions in the world have been committing suicides every moment, his life shows what the life actually means..
Tribute to his Alicia, the lady who realized and lived in love.
Prof. Nash Thank you.....
The entire globe will always remember you......
krj413 (Muskegon, Mi)
Some very sympathetic and beautiful comments here. Such a tragic loss. And while some may not agree with the comment on seat belts, out of this tragedy I hope people start wearing them in cabs and limos.

Beautiful life.
CAMPUS DOC (Connecticut)
Two beautiful minds wasted needlessly. Wear your seat belt!
VIOLET BLUES (India)
Dr John Nash truly enriched the world by his Seminal works on Games theory & countless mathematical postulations that have revolutionised
countless fields in diverse areas of life.
His tragic & horrific death is most sorrowful & truly heartrending.
I send to the bereaved family my sincerest condolences on the untimely demise of Dr & Mrs Nash.
We have again lost an link to heaven.
May their souls rest in eternal piece.
Anon Comment (UWS)
I thought about how Princeton accommodated John Nash during his years of madness. Together with Alicia, they gave him this safe and academic environment that was instrumental in his recover.

I remember Aaron Swartz and how MIT, my alma mater, through its hands-off policy, did nothing to intervene and fed Aaron to the wolves.

We are remembering John Nash. Let's remember too that universities ought to be safe places for free thinking and pushing boundaries.
CraigieBob (Wesley Chapel, FL)
I am very sad to learn of the deaths of a former co-worker, Alicia Nash, and her better-known husband, John. Memories fade with time, but I would like to share some things I recall about this remarkable woman.

When I met Alicia in 1980-81, she was working as a COBOL programmer at Blue Cross and Blue Shield of Greater New York. She seemed over-qualified, but needed a paycheck. She remains the only person I've encountered in business MIS systems who possessed a PhD from MIT in nuclear physics.

Per the dates and ages in this obituary, she'd have already been in her late forties. She was still a strikingly attractive woman, and has since achieved greater celebrity than anyone else I'd met in NYC.

Once, I'd asked how someone with such an Anglo-Saxon surname came to acquire her Spanish accent. She answered simply, "That is [not was] my husband's name."

Later, I learned she'd been riding an ill-fated Princeton commuter train when rails and other materials from a work train moving in the opposite direction smashed through windows of her car, decapitating or impaling some of her fellow passengers. When our teams dined together in the company cafeteria, she was thereafter unable to eat meat, and found it unpleasant to watch others do so.

A loyal and longsuffering wife, she endured a 2.5 hour commute each way, and prepared dinner for husband and son when she got home.

Having mentioned the Nashes quite recently, I found the timing of this news as ironic as it was tragic.
Mac Zon (London UK)
CraigieBob;

Thank you for this written work on Mrs. Alicia Nash. Unfortunately, the NYT missed the opportunity to recognize her contributions and importance to the life of Mr. Nash. Your words has helped all those who have read these comments to understand and appreciate more who Mrs. Alicia Nash was.
andyreid1 (Portland, OR)
Recently I read an article on autism which said the real problem was that when babies are born they have too many synapses in their brains and normally they get eliminated early on. For someone with autism the synapses don't get eliminated and with too many synapses their brains get confused on where to sort the information coming in. After reading that article I've been thinking about that and think some of the geniuses we had such as Mozart and Einstein probably eliminated some of the synapses but had more than a normal person which allowed their brains to make connections a normal person couldn't.

There is a saying that "there is a thin line between genius and madness" maybe it just how many synapses your brain is dealing with at the time.
JP (NY)
Our condolences to the Nash family, friends and colleagues. His work on Topological embedding is still fresh. They were quite a couple.
Paul Kolodner (Hoboken)
Some of the comments I’ve read here about schizophrenia are just off the wall. I read that John Nash was just “differently abled”, “neuro-diverse”, as if psychosis is as benign as sexual orientation. If they had just kept him off the drugs and ECT, he would have been fine, just fine, continuing to do brilliant work inspired by his mystical mental state. All he really needed to get better was good nutrition – presumably vegan. This romantic view of severe mental illness is nonsense. As I and many other Princeton physics/math students in the 70s and 80s can attest, John Nash became a vacant, mute specter, spending his days aimlessly wandering, always wearing the same clothes, unable to communicate with anybody. His intellectual achievements were not caused or enhanced by his disease – they ceased when he got ill, and he was reduced to writing nonsense equations on the public blackboards. If his ex-wife hadn’t been caring for him, he probably would have frozen or starved to death outdoors. Remission in such cases is practically unheard of, and what led to his is probably unknowable. I suggest that we celebrate the miracles of this man’s achievements and his eventual return to health without going gaga over the supposed beauty of psychiatric disease.
Jody (New Jersey)
Bravo. Well said.
Lou51 (Western Australia)
This obituary has generated some unusual responses. Rather than reflecting on the contributions Dr. Nash made, the comments have turned into mini-rants about the wearing or not of seatbelts, the state of New Jersey's turnpikes, the driving abilities of cab drivers, and whether or not 86 and 82 are lives lived long enough. Odd.

Rest in peace Alicia Nash and John Nash.
Easow Samuel (India)
Saddened to read the news that the 'beautiful' couple perished in a car crash. We lost a great mind in Mathematics and economics.
Eric S (Vancouver WA)
In my early years, I had to live around mental illness in a context where I had to decide whether the adult who was responsible for my care was in touch with reality or having a delusion. That is a sometimes frightening experience. Later in my professional career, I would revisit the subject regularly, and sometime I would encounter people who were truly gifted, but mentally ill. Nash's achievements are truly remarkable under the circumstances. I hope his gift gave him comfort beyond the pain he experienced. Life is finite, something which I am sure he had considered, long before his demise. The fruits of his intellect live on. His life was an inspiration.
Sad Start (Mars)
Several days ago, I just found the Game Theory and wanted to study it. But today I heard Nash's death. It makes me very sad. It's a sad start.
The Game Theory tells people how to win the game and get the best result. Strategy is the core. However, Nash died from not tying Safety Belt. So why not think about tying or not, which is the best? Maybe knowledge is good but still needs moving.
VJR (North America)
How many more VIPs are we going to lose in chauffering-related accidents. John Nash and Bob Simon just this year alone. Several years ago David Halberstam. Then there's Tracy Morgans injuries. *sigh* What wastes those three deaths were.
Templardaf (Philadelphia, PA)
I can't agree more.
Steve Singer (Chicago)
Driving is dangerous. Being driven by someone else doesn't make it less. Just because the driver has a license doesn't make him competent or careful.

The list of killed and wounded grows longer by the day.
Luckycharms (Allendale,NJ)
The Nashes have lived a full life. They probably wished they lived longer but they had a great run. Idea was to appreciate John Nash as he was alive, academics did a good job of that but now they seem to create myth-like figure of him. He was too smart for his own good. He also lived in his own world. Can't beat that.
Optimist (New England)
Thanks New York Times,
I really appreciate the links to the 27-page dissertation.
This is a tragic loss to mathematics and economics.
My condolences to the family and friends!
ev (california)
Perhaps one day we will be more tolerant of those with mental illness and make an effort to understand that there is more to the individual than whatever psychiatric diagnosis the person is labeled with. John is a hero in our family. Our thirteen year old son has an IQ of 160+ and suffers from Aspergers. He too has a "brilliant mind" but personality disorders that make him "abnormal" in our society. Perhaps one day, like John Nash, he will achieve his dream, a Nobel Prize in Psychics. John Nash, thank you for having your story told and thank you for providing hope and inspiration.
gcb (Boston, MA)
"We" - speak for yourself. How big of you to ponder the notion that one day "we" will tolerate people with mental illness. Those with mental illness want to be more than merely tolerated, ev. People with mental illness need to be accepted, not tolerated.
ev (california)
Sorry for the typo. Physics not Psychics.
JM (CT)
Hang in there. I have worked with so many people with Asperger's who have grown up to be great contributors to society and have found their niche in this world. All too often, schools have a a narrow view of what constitutes normal, but many people with Asperger's lead fulfilling lives once they finally break free of the shackles of elementary and high schools.
ondelette (San Jose)
Because I'm a little divorced from economics, I am more familiar with his embedding theorem (the one about the "squishing"), but was aware of what the game theory result was and that it was considered important. Interesting that the consensus is that the embedding theorem was his finer work.

I am very sorry to hear this news, I do wish that people would work a little harder to appreciate his life and that of his wife, and not be so fixated on seat belts.
Madigan (New York)
Let us ponder a little on the seat-belt, or no seat-belt, as in London's cabs. This tragedy would not have happened in London, as the cab drivers and their cabs are fully scrutinized to follow the rules, long before they get their cab driver's licences. Having experienced similar fast and dangerous Service-car rides here in Manhattan, and upon request to the driver to slow down, I received a well practiced response on several occasions: "Sir, I have to pick up more passengers after I drop you off, to help me pay for this car". I would hold the Taxi Licensing Commission (TLC, an unfortunate name), fully responsible for this great tragedy.
Madigan (New York)
Let us ponder a little on the seat-belt, or no seat-belt, as in London's cabs. This tragedy would not have happened in London, as the cab drivers and their cabs are fully scrutinized to follow the rules, long before they get their cab driver's licences. Having experienced similar fast and dangerous Service-car rides here in Manhattan, and upon request to the driver to slow down, I received a well practiced response on several occasions: "Sir, I have to pick up more passengers after I drop you off, to help me pay for this car". I would hold the Taxi Licensing Commission (TLC, an unfortunate name), fully responsible for this great tragedy.
Richard (Bozeman)
I had the same response about the relative significance of his theorems. In fact I first ran across the Nash-Moser implicit function theorem in his work, equally brilliant and absolutely ignored in the movie and all columns I have read. Such is the fate of pure mathematics.
LT (New York)
Great sadness.
Is there an "irreverent" meaning in the uncanny hand gesture/posture of John Nash on the Princeton Graduation photograph? An defiant distance to the solemnity of the occasion or to the academic recognition of his exceptional gift? In any case it is a very moving document and an enigmatic image at the same time.
RCT (New York, N.Y.)
I have long admired John Nash. The seat belt comments here are beside the point, and offensive. Virtually no one wears seat belts in taxis and limos. Yes, they should; but no they don't. The Nashes death was senseless and arbitrary. Even a brilliant mind can't protect you from a stupid, random accident.

It is tragic, too, that their son and Nash's son were unable to say goodbye. That John and Alicia were in their 80s is irrelevant; their lives were full, and their families are shocked and grieving. All deserved better than this.
gcb (Boston, MA)
The age of people in their obituaries is the norm whether irrelevant or not.
Jody (New Jersey)
You are absolutely right that the Nashes being in their 80s is irrelevant. They were obviously participating in life and enjoying it. Let's call out ageism when we see and hear it. But I beg to differ about seat belts. Those of us who travel in taxis or cars on the NJ Turnpike wear seat belts -- at least, everyone I know does. The road is in dreadful shape with many cement dividers on both sides, which narrow the road, making it dangerous as too-big-not-to-crowd monster trucks and cars barrel down at 70 m.p.h., and often much faster. I'm sorry and saddened that it took the life of these remarkable people.
AHW (Richmond VA)
The seat belt comment is not irrelevant as it could have been anyone in that back seat and the loss of that person just as tragic. I am not discounting the Nashs as they are truly legends but this should be a lesson to wear your seat belt even in the back seat even in a cab/limo.

Working in a trauma center we often see where the belted passengers while hurt are still alive unlike their unbelted friends. May their tragic deaths serve as a lesson to others just as his mathematical solutions served another kind of lesson.
S B Lewis (Lewis Family Farm, Essex, New York)
Bless Sylvia Nasar for her devotions. She is the rarest of reporters: sincere and thoughtful, caring and honest.

Bless John Nash and his beautiful wife for her courage and devotion and his courage and brilliance. He is not the first, nor will he be the last.

But she may be the first... for her loyalty and understanding of her man.

I found the move too painful. I left in tears half way through.

Those that experience such hardship can often return to a world they left and make it a little bit better. They they do not forget what put them where they were.

We cannot forget, we just think we can. It's all there...

What a terrible loss. These two did it all... and did it so well.

And so tastefully.
survivalist 13 (las vegas)
I kept in contact with john, although he didn't write back he's IP address showed up on my website. I'm crushed like john I to was sick and after 20 years of hospitals Ive recovered to a certain extent. He will always be remembered. The last time I wrote him was with my theories, I kinda wish I had said something a little more personal. My warmest regard to Johnny and john and their sister. Truly the Best, it's a sad day in my life, I wanted to meet him. God Bless you Alicia for standing by your man. Two herrific loses. Rip
Ordinary Person (USA)
The book on his life was one of the very best books I've ever read.
L.Tallchief (San Francisco)
It was wonderful, and remarkable in that John Nash refused to be interviewed. But he was ultimately very happy with the book and thereafter gave his blessings to his friends and colleagues to speak with Ms. Nasar. Her work was surprisingly good, especially given the handicap of being unable to speak with the subject of her work.
Elizabeth Guss (New Mexico)
I have long held Dr. John Nash to be among the pantheon of the truly brilliant. Nash, Einstein, Bohr, Schroedinger,Oppenheimer -- these were gifted minds that saw beyond the ordinary. How lucky we are to be the recipients of the fruition of their gifts!

The world is diminished by the death of John Nash, and his wife Alicia as well. How sad, though, to think that one so brilliant, and his steady helpmate, could be snatched from our midst for the apparent neglect of wearing seat belts.
suzin (ct)
Sad to learn of this violent end, but they went together and I guess that is the only solace. Would like to see her obituary too? Hope it's in tomorrow's paper
Alan Carmody (New York)
While economists claim John Nash as one of their own, and indeed he was a recipient of a Nobel prize in economics, John Nash was first and foremost a great mathematician.

It was but one of his great mathematical accomplishments, in game theory, that economists found so powerful and useful. But mathematicians would argue that his work in differential geometry was the greater intellectual accomplishment.

While he did not receive the Fields medal, the greatest honor for mathematicians under the age of 40, John Nash was awarded the equally prestigious Abel prize for mathematics by the King of Norway just a few days ago. That must have been some solace in his old age, solace that he, tragically, enjoyed for but a few days before he died on Saturday.

Rest in peace, John Nash.
Yayi Carles (Panama)
When I got my BA in chemistry and mathematics in 1980, A Beautiful Mind was not even scripted but by then John Nash had already created the foundation for confronting various unsolved problems in real life. It was in 1996, when I became the commissioner of free competition in Panama, that I first applied one of his theories to solve collusion in non competitive markets. Everyone speaks now of Nash as a brilliant mind... but the fact of the truth is that almost no one has read - nor understood - his graduation thesis. I congratulate The Times for presenting the link to it and giving one more time the opportunity to show us how monumental he was.
fast&furious (the new world)
So many people are called "heroes," "geniuses," "courageous" or "inspirational" that these expressions have become overused or trite. But John Nash truly was all three.

The Nashes were the stuff of legend. So sorry they are gone.
JBK 007 (Le Monde)
You mean, he was all four, basic math, same principle.
JM (CT)
I agree: The Nashes WERE "the stuff of legend." I am troubled that I can't find an obituary of Alicia Larde Nash on the pages of the NYT. I truly hope it's my oversight; however, a search of the website has not turned up her obituary.
Clyde Wynant (Pittsburgh)
The year before "A Beautiful Mind" debuted, I encountered a man at an intersection in Princeton. He was slowing crossing the street in front of me. I was taken by the man's diffidence and, at the same time, his strength; for he gave me a look that seared into my mind. I believe that man was Professor Nash. I remember the moment as if it were yesterday. God's speed, Professor.
Frank Wang (Oklahoma City, OK)
I was an undergraduate math major at Princeton from 1982-1986 and saw Nash at the Fine Hall Library (the math and physics library) all the time. In the beginning I didn't know who he was. Once, he got in the elevator with my undergraduate advisor Prof. Bernard Dwork at Fine Hall and remarked how good the coffee was. When got off the elevator, I asked my Prof. Dwork who that strange man who hung around the math library was. He responded "Don't make fun of that man. He was a brilliant man who once taught at MIT...." He explained about Nash. Fast forward a bunch of years; I now head up a selective public residential school in Oklahoma (similar to Stuyvesant HS in NYC except that we are residential) called the OK School of Science and Math (OSSM). I spoke with Nash a few months ago and invited him to come and be honored and speak at OSSM as part of our 25th Anniversary Gala. I shared how I taught the students in my "Special Topics in Math" class about the Nash equilibrium. (I shared that he would likely recognize me from my student days since I spent so much time at Fine Hall and reminded him that I had stopped by his home in the mid-2000s.) I offered to come and personally escort both him and and his wife to Oklahoma City where my school is located. He shared with me that he had a distant relative who lived in Oklahoma whom he had not seen in some years and might like to look up. If not for this tragedy, he likely would have come this coming academic year.
boganbusters (Australasia)
God bless you!
bnc (Lowell, Ma)
Having worked in a research environment, I have observed many of the men and women with doctoral degrees had strange habits. One man rode his bicycle to work and trimmed off the mud-stained part of his tie after a trek in the rain; my boss paced the floor like an expectant father, saying he was waiting for a memo to be approved. A skit was done of a college psychology professor who habitually packed and unpacked his cloth book bag as a sort of "Mr. Rogers"; everyone knew who the student in the black trench coat was spoofing.
gcb (Boston, MA)
How nice people make fun of people who don't act like many others...if you your comment is true. I think the people involved are pathetic. People need to stop making fun of others just because they may exhibit behavior that appears to be beyond the norm.
Chrislav (NYC)
First 60 Minutes' Bob Simon on the West Side Highway, and now Dr. and Mrs. Nash on the NJ Turnpike.

Such wonderful, smart people who might still be here if they had buckled their seat belts.

Next time you think of not buckling yours, please think again.
Lulu (New York)
A terribly sad event.

My life, and my father's life, have been saved with seat belts, in separate events.

When I was young, every weekend going to visit our grandparents in the country, getting away from NYC, there was The Magic Key to start the car. The Magic Key only worked if our seat belts (during the era where you had to pay extra for them no less) were connected.

I have told the Magic Key story to many folks and family with young kids. And it seems to still work!

Goodness knows if this tragedy will bring forth anything good, other than making folks use their safety belts! I mourn the loss of two people have had a life more difficult than I could possible imagine. They deserved more time at peace.
James (Northampton Mass)
Letterman gone, now this. Nash was an amazing soul. Odd death, but with his beloved. Life is strange and beautiful.
Gordon (Nashville, Tennessee)
So you're comparing Letterman's retirement from Late Show to John Nash's death?
Christine (SFO/PHX)
Thank you, James.
Faith (Ohio)
I have not watched A Beautiful Mind but am compelled to read Sylvia Nasar's biography of this complex personality. Dr. Nash's own observation is most provocative, that the natural sway of hormones directed a return to rational thought. I am taken aback, too, that the state of mental balance could have been an obstacle to awarding the Nobel; that as recently as the 90s, the stigma toward neuro-diversity was so profound. Even as the journey remains long, we have traveled far.
gcb (Boston, MA)
I am also taken aback by the idea that he may not have been awarded he Nobel. Had he been suffering from cancer would they have even given that a second thought when awarding him the Nobel? People need to stop stigmatizing mental illness.
Steve (New York)
Anyone who knows anything about mental illness knows that it is highly doubtful that Mr. Nash never suffered from schizophrenia. Most likely he suffered from bipolar disorder. There have been people with bipolar disorder who have managed outstanding achievements despite their illness even when Mr. Nash was a young man; there were virtually none with schizophrenia who were able to do so and even now with modern medications it is still very rare.
And I wish The Times would once correctly name what it calls "electroshock therapy." The shock comes from insulin shock which was the original way the convulsions were induced. With electricity, it was and always has been electroconvulsive therapy.
DW (Philly)
But the paranoid delusions? His paranoia was quite severe I think.
Jersey Mom (Princeton, NJ)
The Nashes live a mile from my house in Pirnceton Jct. For years he used to wander over from his house and stand on the sidewalk next to the Acme talking to himself and waving his arms. He says himself that voices spoke to him. (Colleagues at Princeton first started to worry about him when he told them he might be elected Pope). He was not bipolar. He was schizophrenic. The achievements for which he won the Nobel Prize were all before the disease began to manifest itself. After that, for decades he did nothing at all except wander the streets conversing with his voices.

No one should ride in a car -- even down to the end of the block -- without a seatbelt. The daughter of a friend of mine was in her boyfriend's car while he was parallel parking and she unsnapped her belt when he pulled in and then he decided to reposition the car so he pulled back out of the spot and a car came along behind them and smashed into them and she went through the windshield. She had 20 stitches in her face. And her car was going 0 mph and the other car probably only 40. Seat belts should be worn whenever the engine is on.
Brian (Wallingford, Ct.)
Paranoia can be very strong with bipolar disorder.
HRL (New Jersey)
t is only news when famous people die or are seriously injured on the New Jersey Turnpike near Exit 8A in Monroe Township. The math genius. The comedian. The Exit 8A area is probably the most dangerous section of the entire highway. Something must be wrong with the way it is designed and built. Many people die there. Many people suffer injuries so severe that they wish they had died there. Yes, it is a sad ending for the story of Dr. Nash and his wife. It is also sad that nothing has been done, nothing is being done and nothing will be done to alleviate the dangers of this section of the Turnpike. It is sad that more people will die there.
FFILMSINC (NYC)
lets all do something NOW - I will!
FFILMSINC (NYC)
Both John and Alicia Nash were remarkable human beings, whose stellar work, belief systems, conscience, ethics, humility, grace and extraordinary intellect were a gift to all of us who admired, respected and understood their powerful mission and authentic vision

Our hearts go out to their family, friends and the academic community supporters

This is a tragic and great loss that should never have happened

Rest in Peace John and Alicia

You will never ever be forgotten
Lambert C. Timmermans (Brussels, Belgium)
Quelle triste loi des hasards,
que d'intégrer ainsi
la mauvaise trajectoire,
d'un taxi nommé gâchis.

What as sad tragedy,
in the rule of randomness,
to integrate the bad path
and resulting poor trajectory
of a taxi called messy.

R.I.P. Dr & Mrs Nash.
Psych Survivor (USA)
I am deeply saddened to learn that one of my role models has passed away in such a tragic manner. Learning about his own struggles helped me greatly in my own recovery.

For those of us labelled, and stigmatized, with invented psychiatric diseases, John Nash was a candle in the dark represented by the American Psychiatric Association. Where the APA offered a life of drugging and hopelessness, Nash offered the triumph of the human spirit over our deepest demons.

Whenever I felt low I always watched the PBS documentary on his life "Brilliant Madness" to remind myself that we are better than then labels listed in the DSM: first and foremost human.

God Bless John Nash. RIP.
Margo (Portsmouth, RI)
No one with mental illness should be stigmatized. But to state that physicians "invent" psychiatric diseases is a slap in the face to the dedicated professionals who treat these patients. Science is slowly unraveling the mysteries of the brain, our most complex organ. Instead of demonic possession, or smothering parenting, research is showing that many, if not all, mental disorders are due to neurochemical anomalies. Many depressed people have a happier life because of medication--a far cry from "drugging and hopelessness." Treatment of schizophrenia has improved, although not as greatly as with depression. Not all delusional people need drugs, especially if they are not a threat to themselves or others. But too many schizophrenics have come to harm or harmed others because they stopped their prescription drugs. One can't say for sure that Dr. Nash overcame his illness simply by deciding to be rational. Perhaps with time, his brain chemistry corrected itself. But whatever his case, there are many mentally ill people who need medication. The side effects are well worth saving lives.
Steve (New York)
Yes, let's not treat anybody with mental illness and simply rely on "the triumph of the human spirit" to cure them. And let's not diagnose anybody either. Even better, let's go back to believing mental illness is the result of demonic possession.
Psych Survivor (USA)
Institutional psychiatry has not provided any proof - that would be acceptable according to the standards used by other areas of medical science such as HIV science- that what it calls "mental illness" is caused by a chemical imbalance in the brain. None. The APA admits this if you read the statement produced by David Kupfer in the aftermath of the DSM-5 controversy caused by the NIMH abandonment of the DSM for its lack of validity. The former Chief Editor of the Psychiatric Times. Ronald Pies, also has admitted this, but he denies any responsibility from institutional psychiatry in promoting the idea that it calls "mental illness" is the result of a chemical imbalance in the brain. Your comment disproves his assertion.

You claim that psychiatry saves lives, but again there is no proof that that is the case. John Nash drug free recovery is not an exception, if you study the work of Harrow and similar. In fact, a recent study published in the peer reviewed New Zealand and Australia Journal of Psychiatry asserts that "US Food and Drug Administration–based analyses demonstrate that almost all atypical antipsychotics and anticonvulsants are carcinogenic in animals, as are the majority of antidepressants and benzodiazepines and methylphenidate. These animal-based results are not sufficient to draw definitive conclusions in humans, but they provide data that could be acknowledged in the informed consent process of clinical treatment." So very likely the reality is the opposite.
skanik (Berkeley)
A sad, odd and tragic ending to a unique life.
Monique Falcão (Rio de Janeiro)
I wish I had studied maths to better understand Nash's theory. I sound so beautiful.... In human sciences, this theory is used to comprehend how we distribuate rights ands goodness. But we study it supperficially..
Jake Gelfand (NY)
They may have not been officially married for part of those sixty years, but theirs was a long and great love story, nonetheless.
http://goo.gl/kWUjU6
Spencer (St. Louis)
It is never too late. There are even online courses, through Coursera and EdX, you can take for fee. Introduce yourself to the beauty of maths.
Marcos Mota (NYC)
I am sorry for the loss to his family and academic community, but just recently Bob Simon died while not wearing a seat belt.

Twenty years ago we lost a friend who was ejected from a van. To this day we remember her every year and make it a point to wear our seat belts. It is so easy to get ejected from a modern car, that your oversight will likely cause you great injury. Also, just because you are a passenger, don't let the driver be the only one in control of your fate. If you keep an eye on traffic and ask the driver to make corrections, it establishes that you are in charge. I do it all the time on the BQE and the WSH while in a city cab. If they ignore you, they risk affecting the tip amount. Also, yellow cabs are more visible than (usually) black Uber vehicles. Just pointing out a small benefit.
David Chowes (New York City)
BEHAVIORS ARE MULTIDIMENSIONAL

That is why a test which is focused on only one area cannot encompass the range of a person. A simple example: one can get a perfect 800 on the verbal part of the SAT and far below average of the quantitative portion.

So, never assume that a psychotic person is deficient in all ways. In Sylvia Nasser's book. "A Beautiful Mind" and the film of the same name.
Concurrently, Mr. Nash was both delusional and hallucinating and was simultaneously arriving at game theory insights which led Nash to receive the Nobel Prize.

Dr. Nash was suffering from what would be diagnosed as either schizophrenia or bipolar disorder are the constructs we presently use use to identify his aberrant behaviors. But, in terms of what IQ tests measure, probably in the highest portion of 99th percentile.

Working as a psychologist in a state hospital, a man was admitted who the average person would describe a quite crazy and mute. He never responded to questions and attendants had to do all the basic tasks for him.

One psychiatrist would hear him mumble numbers; one day the doctor realized that they represented the first 15 or so digits of pi. We later determined that he was a professor of mathematic at a university.

The is the old saw that there is a fine line between genius and madness. And, there is empirical evidence of this: read Dr. Kay Jamison's "Touched With Fire" which posits that in many cases of serious mental disorders, there is twice the chance of genius.
Steve (New York)
There have been many very successful people with bipolar disorder; there have been virtually none with schizophrenia. These are two very different disorders.
David Chowes (New York City)
"Steve," You are correct. To be more specific, it is those who have mood disorders (e.g., clinical depression, bipolar and its variants. E.g., Emily Dickenson, William Styron, Art Buchwald, Robin Williams, Oscar Levant...

And, Kay Redfield Jamison, Ph.D. (who has been a professor of psychiatry at Johns Hopkins University for many years and has suffered from bipolar disorder** since her teenage years). She is co-author of "Manic-Depressive Illness," a 1,000+ tomb on the disorder and considered to be the definite book on this disorder.

**Note: manic-depression is now referred to as bipolar disorder.
scientella (Palo Alto)
This is not true. Schizophrenia is a diagnosable disease with quite specific symptoms, age of onset prognosis etc. Its not a black box. Whats more some reasearchers are zeroing on possible causes. Its disruption to the development of the brain in a specific way at a specific time , hence it predictable age of onset. To give the much needed help to the many millions suffering from this disease we dont need misinformation we need scientific research.
The person who unravels this will have done one of the greatest services to mankind. Better than game theory.
Anon Comment (UWS)
This is how it ends with John Nash. How he would hate it that his death was random.

I remember the 1st time I read A Beautiful Mind on a long haul flight from San Francisco to Southeast Asia. I read the 1st chapter that summarized John's life with a bang. I was so moved, I read the entire book in one go on that flight.

I then studied in MIT in 2002 which was right after the movie won many Oscar awards. And many of us new students wanted to learn about game theory.

- MIT alumni
Karen (New York)
How sad. I'm glad he won through all this but I can only imagine how great the cost.
Vanessa (Massachusetts)
And the cab driver ... dead? alive? injured? Does his life not matter?
szinar (New York)
Vanessa, set your mind at rest. The answer to your question is in the third paragraph.
P Desenex (Tokyo)
From one of the first few paragraphs of the obit: "The taxi driver and the driver of the other car were treated for non-life threatening injuries."
No one's fool (Northeast U.S.)
It shouldn't. He was the one who *caused* their deaths. If better attention to the reckless driving so common among East coast big city cabbies doesn't come about as a result of this, their deaths will have been very much in vain.
Rohit (New York)
I remember seeing John Nash and his wife on LIRR going to a conference at Stony Brook where I too was going. I noticed that some people asked him for an autograph and one or two wanted to be photographed with him but no one helped him with his large suitcase. (I myself am quite old or I would have helped).

I know for sure that this would not happen in India or China and there, perhaps is an explanation of the Asian miracle. A sense of community and of what we owe to others. I know that this sense of what we owe others still exists in American hearts, but it has disappeared from American culture.

I had several chats with him during the last ten years or so, and always found him to be a modest man, easy to talk to and not at all conscious of his fame.
AC (Cambridge)
Dear Rohit,

I am from India (in US for 9 yrs now) and I disagree with your comments. The suitcase situation likely arose because Americans deeply value individualism and self-reliance. During my early days in US, I tried helping senior members in situations like you mentioned and soon realized that many were offended.

I am also confused by “Asian miracle”. I agree that Indians who have immigrated to US have done well compared to their counterparts in India. But doesn’t that speak well of American culture?

Most Indians who immigrate to US come from very educated and/or well-to-do families. As such, they have primarily experienced refined aspects of the Indian culture. However, most of India is poor. If one grew up in a low/middle-income family (or low caste/one of India’s pariah states), I have first-hand experience that the indifference of Indians will make you cringe. I am proud to be Indian, but I don’t let my pride cloud my objectivity.

With kind regards,
AC
Rohit (New York)
Here are two more examples. I was going to a seminar at Columbia and I knew the building but not the room. When I arrived at the building, two Chinese students met me, and without a word, one of them took my backpack and carried it.
It is quite common for Chinese students to carry their professors' backpacks and when I was in China, one Chinese girl carried my backpack for nearly two hours.

When my mother was ill, I flew to Ahmedabad and my flight was arriving early in the morning. Two men left the town where my mother was, arrived in Ahmedabad airport at 4 AM and slept in the car till the plane arrived. Then they took me and my stuff to the hospital where my mother was. And no, they did not expect any money.

I find it shocking that Nash, who was then 84, should have been allowed to carry his own heavy suitcase in the name of individuality. It is not respect for individuality, it is simply callousness. He deserved better.
Rohit (New York)
" I agree that Indians who have immigrated to US have done well compared to their counterparts in India."

Didn't you leave out a MORE relevant fact that Asians who have immigrated to the US have done better than other minorities?

American culture cannot explain that so easily can it?
Merlin (Atlanta)
Very sad. Dr. Nash's story is one that I really admired and told repeatedly. A couple of months ago when asked my favorite movie, I quickly said "A Beautiful Mind". Two weeks ago I told the story of his brilliant mind to a friend.

Sometimes life is very unfair. A guy like John Nash and his long-suffering, faithful wife do not deserve a violent death.
MCE (Wash DC)
Yes, it is very sad that they died.

But I would personally prefer the way they died to the many more likely possibilities (such as spending months in a hospital or hospice, having Alzheimers, etc.) Considering all the alternatives, not a bad terminal move, especially considering they were a couple
to the end.
DW (Philly)
I agree, MCE. If you've spent a lot of time around elderly people dying very slowly, in a years- or even decades-long process of slow decay and debilitation, as awful as it sounds dying suddenly well into one's 80's doesn't sound so terrible. Of course his death is sad, though. And his wife was a bit younger. On the other hand, this way, they will never be separated, and neither will know the pain of losing the other.
irate citizen (nyc)
I was in Vienna and didn't fasten my seat belt properly in the taxi. An alarm went off and the driver stopped and told me to fasten it correctly. Unfortunately, that is not available in cabs here in NYC as there should be.
Mindy Newell (Bayonne, NJ)
My daughter, son-in-law, grandson and I were driving home yesterday. We saw the accident.

I am sick.
Tblumoff (Roswell)
I could never have imagined a man who's genius and torment would mean more to me than John Nash, and his story. Nash's experience kept my life with a brilliant and/but disturbed individual going. Sylvia Nasar biography is must reading. RIP, John and Alicia: RIP at last. KAK
Keeping It Real (Los Angeles)
John Nash's story is first and foremost a love story. Very few people will ever experience the kind of devotion his wife Alicia showed to him despite his deep mental illness in his younger years. Both of their stories are a powerful testament to the strength of the human spirit.
Kay Tee (Tennessee)
She had a heck of a time with him and did divorce him.
Steve (New York)
I would disagree. There are many families that have been very supportive of people with bipolar disorder, which Nash probably had. It is much more difficult for family with members who are schizophrenic to be as supportive because schizophrenia can so severely disrupt lives that it is impossible to maintain anything close to normal relationships. And bipolar disorder is much more treatable than is schizophrenia.
j. von hettlingen (switzerland)
May John Nash rest in peace. I'm not a mathematician, but I'm familiar with his "Nash equilibrium".
The world may have been more peaceful, if conflicting parties could adopt his theory, instead of settling for a zero-sum game!
math365 (CA)
From an article in the New Yorker on attempts to interview Fields Medalist Grigory Perelman.

"We took a taxi to his apartment building and, reluctant to intrude on his privacy, left a book—a collection of John Nash’s papers—in his mailbox, along with a card saying that we would be sitting on a bench in a nearby playground the following afternoon."

I find it amazing, inspirational and motivating to read of great minds challenged by great obstacles and achieving great accomplishments: Nash, Hawking, Perelman, Beethoven, and too many others to list. Even at 86 and 80, Nash and his wife left this world when they were too young.
Geoff Knauth (Williamsport, PA)
I met him five years ago. He was a very kind man, and I will miss him.
DJS (New York)
“ His brilliance turned malignant ,leading him into a land of paranoia and delusion,and in April ,he was hospitalized at Mclean Hospital,sharing the psychiatric ward with,among other,the poet Robert Lowell.”

Brilliance is not the equivalent of a pre-cancerous polyp,which,barring removal, turns into full blown cancer .

Brilliance does not “turn malignant .” Brilliance does not mutate into Schizophrenia. It does not" lead people into a land of paranoia and delusion, resulting in hospitalization in psychiatric wards ."

John Nash was a brilliant man, who ,coincidentally, suffered from mental illness. There are numerous individuals who are not brilliant or even intelligent,who suffer from mental illness,and brilliant people who suffer from no mental illness.

The author continues to suggest a correlation between genius and mental illness ,and even to romanticize it, in my opinion,with his unnecessary mention that Robert Lowell was a psychiatric inpatient at McLean at the same time. This is supposed to be about Dr.Nash’s tragic death,and his life, not the “who’s who” of inpatients at McLean Hospital.

If Dr. Nash and Robert Lowell had both received Nobel Prizes at the same ceremony ,the mention of Mr.Lowell would have been relevant. In this context,it is no more than gossip;

Psychiatric illness is an equal opportunity illness,just as cancer and other illnesses are.
Lisa VanHevele (Clinton Twp, MI)
Why not critique the contents and not the grammar? DJS's comment is relevant. Your's however is not.
srwdm (Boston)
Excellently reasoned and stated.
Anon Male (San Francisco, CA)
No, DJS is right. If Nash had cancer or AIDS, the author would not say "sharing the wing with Lindsay Lohan [or whoever]." It may be subtle but there is a romanticization of mental illness here and perhaps of brilliance, both perhaps not in a good way. They are both ways of separating people with these traits from what is considered "normal".
chiliyo (St Pierre et Miquelon)
Tia Alicia and John may you both and your brilliant minds rest in peace for ever.
Alberto (New York, NY)
As a psychiatrist I want to point out here, for those interested in Dr. Nash and in Science in general, that the "diagnosis of Schizophrenia" which was given to Dr. Nash, is not based on strict scientific knowledge.
According to the knowledge and criteria available since 1959 to the present, the way the diagnosis has been asigned to people everyday has been, and still is very defective.
Through the years psychiatrist have handled Psychiatry not as a science, but as a field where scientific rigor is not demanded because until now most people give a pass to the study of the mind as a mixture of art, biology, and metaphysics or spirituality. So in psychiatry practitioners are allowed to claim prestige and profit without scientific rigor, and that unfortunately for some, and profitably for others, has kept psychiatry as an uneven mixture of theories some of them cult-like, such as psychoanalytical theory and Jungian theory, while other theories are based on partial knowledge of basic biological sciences such as physiology and biochemistry.
Besides, the approach to psychiatric treatment was initially based mostly on flimsy ideology, and then on trial and error, instead of on fundamental understanding of the way the brain works.
Up to present, there is only partial knowledge of the way the medications and psychotherapies, which are prescribed every day to millions of patients all over the World work.
Tblumoff (Roswell)
Then begin advocating for better science, Doc.
jan (left coast)
Thank you.

I think it was possible that he was misdiagnosed, mismedicated, and mistreated.

As for the seatbelts, they often just aren't there in taxis.
Lisa VanHevele (Clinton Township, MI)
Seat belts should be required front and back in all vehicles. They were thrown from the vehicle and much more likely would have survived had they been belted in.
Shawn (CA)
Yes, I understand it might be difficult to fasten the seat belt for aged people. But why not, even it may take 10 minutes. Great loss for the whole mankind.
kat (New England)
I'm an "aged person." It takes me maybe ten seconds to fasten a seatbelt.
outis (no where)
I think in some people's minds, taxis are somehow safer because a "professional" is driving? Maybe they seem to be like other public transport, where no seatbelts are used? Or then again, perhaps it was not available? I do remember getting into NYC cabs not so long ago and not seeing the seatbelt because it was unavailable, tucked into the seat. Maybe because it is not mandatory, few use them and they are not always out. When Bob Simon, also not wearing a seatbelt, was killed in the taxi cab crash, it was said he was not violating the law: http://www.usatoday.com/story/news/2015/02/13/no-seat-belt-violation-in-...
Princess Diana also was not wearing her seatbelt and had a driver.
Lisa VanHevele (Clinton Township, MI)
Why would we trust some unknown driver to take us anywhere in an automobile where we don't have to wear our seat belts. Jeez, we have to wear them on a plane where we are much less likely to die in a crash.
Kevin Hill (Miami)
Professor Nash's work on non-zero sum game theory revolutionized the social sciences. Even though this was sometimes not for the better, that;s not his fault!

RIP Professor Nash and Mrs. Nash.
JB (NJ)
As an economist that admires his work and a driver that uses the NJ Turnpike everyday this really upsets me.

His work explains how we make decisions everyday. His death on the turnpike explains how dangerous that roadway is.
Mozee (NYC)
Turnpike is one of the safest highways in the world.
outis (no where)
Is it really? It sure seems unsafe.

However, the decision to not wear a seatbelt was unwise.
Bob (Portland, Maine)
I assume that's a joke.
Arnab Sarkar (NYC)
To understand the slow Economic growth around us, consider the following statement as put by NYT "...he arrived at Princeton in 1948, 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....".

I have read about the heydays of Feynman, Dirac, Pauli and others and have always admired them. Back in India I also read about Raman (Nobel Prize in Physics, 1930).

What are children (American or anywhere over the world) dreaming of growing up to be?

I recently had a talk with a nephew and neice back in India. The nephew insisted on focussing on Physics and my neice in Computer Science and Mathematics. I wished them well and asked them to enjoy some classic movies if they have time. One I recommended was "A Beautiful Mind".
sweinst254 (nyc)
"Jane Austen wrote six novels." That's a brilliant analogy. The greatest minds leave very few works but perfect ones.
LR (Oklahoma)
Six novels is "very few"?!
srwdm (Boston)
How poorly we understand the caverns and recesses and reaches of the human mind.

A four chambered heart to be valved or re-fitted it is not.
Sal (New Orleans, LA)
John and Alicia Nash suffered a tragic end to their triumphant trip to Norway. Seat belts can be difficult to operate as one ages. Drivers could routinely arrange the belts on the seats and offer assistance with the buckles. Often I find only the belt or only the buckle visible on the back seat of cabs and cars. Every make is different. So the cabs speed off and the passengers take the risks.
stevenz (auckland)
*Definitely* an issue with taxi cabs, then add in driving skills of most cab drivers...
L.Tallchief (San Francisco)
My father, Prof. Nash's psychiatrist, was one of the "friends and colleagurs" who received cryptic postcards (and letters) from him during his stay in Europe. Always playful, he would address them to Docteur Pommes, translating his Italian surname into French. Following his treatment and throughout his recovery, he remained friends with my father, who still resides in Princeton. I will always be sorry I didn't have a chance to ask him if he remembered sending the three fortunes ("Reading Hurts On One") from his fortune cookie to Trinity Bookshop in NYC. They were returned to the return-address, as engraved on the envelope: Institute for Advanced Study in Princeton, which promptly forwarded them to my father. He got the joke immediately.
Steve (New York)
So it was your father whom many of the commenters appear to consider the evil person who mistreated Mr. Nash with unnecessary psychiatric treatments. I guess that's why Mr. Nash considered him a friend.
CAMPUS DOC (Connecticut)
Your comment, well no doubt well intentioned, is an invasion of professor Nash's private history, in particular the history of his relationship with his psychiatrist. Had your father written the comment, he would face potential censure.
scientella (Palo Alto)
Like Steven Hawking John Nash's illness was made a whole lot easier. Pity others with debilitating illnesses who did not do brilliant things in their youth. This should be an opportunity give support for the reopening of institutions which give true asylum to schizophrenicsill then emptying them onto the streets where they cannot look after themselves or destroying whole families with the burden of medication and care and the constant risk of harm. 1.5 in a hundred have schizophrenia and the advanced worlds response is to give them a prescription.
April (New York City)
"Stigma" is not a good word to use when trying to decrease prejudice against the mentally ill. Only in regard to mental illness is "stigma" is used. It increases, not decreases. prejudice felt by mentally ill patients. Even if they are geniuses, as of course, most are not.
PA (Albany NY)
His recognition of his work with a Nobel prize, and now an Abel Prize, and is dutiful wife remarrying him together is Poetic. Hollywood would not cash in any other type of a Mathematician. His consultancy with RAND is what is being used by Pentagon in Surge etc. Also, Game theory is used in plea bargains.
MTF Tobin (Manhattanville, NY)
.
.
Two beautiful minds -- and an extraordinary partnership -- ended on the New Jersey Turnpike. Wow.

I am comforted to know that they were together; and also, that last week Dr. J. F. Nash, Jr. was being awarded the Abel Prize by the King of Norway. Wonderfully fitting.

I would also imagine he could have calculated the competing interests of the drivers on that road, and the odds that a fatal collision would occur; while she could have explained the interaction of forces inherent in such a collision. They were that good.

I hope they were looking at one another just before the accident.
Blue State (here)
At 86 and 82, I can think of worse ways to go.
outis (no where)
Perhaps you are right. Perhaps it was a good death, and for them to go together, suddenly might have been the best of fates.

But I would bet they would not have chosen it.
Denis McDaniel (San Diego)
Right. At least they went together. That's something. Neither had to grieve a loss.
Harvey Liszt (Charlottesville, VA)
Wear your seatbelt, even in the back seat of the taxi.
Elle1971 (Hoboken, NJ)
Many great Artists, Musicians, and Theoroticians such as Mr. Nash suffered with some form of 'Mental Illness' including Schizophrenia and Bi-Polar Disorder. Kay Redfield Jameson has authored several books about people who had, or have, Bi-Polar Disorder. Some of these people are alive today and speak about it freely. The late Robin Williams spoke about it often in his performances and David Letterman has spoken about his Bi-Polar Disorder too. He tells the story of going to the Store in his Pajamas and not thinking anything was amiss.

It is tragic that Dr. Nash died in such a violent manner but he has left a Legacy of his brilliance.
Steve (New York)
There have been many with bipolar disorder but virtually none with schizophrenia.
A. Stanton (Dallas, TX)
Musings occasioned by the untimely passing of John Nash and his Mrs.
1. Cabs shouldn’t be able to start until all passengers have secured their seat belts.

2. I had considerable difficulty with calculus, but never have had much trouble making the money I need to get by. Go figure.

3. What’s going on in that graduation picture of his? I’ve never seen another one exactly like it.
A crude joke maybe or some small preview of his future problems?

4. Economics being the mostly bogus science it is, I wouldn’t be surprised if someone comes along soon with proof positive that Nash’s theories are mostly bogus. (Not that I myself would ever know or care whether the new guy’s proof positive was also mostly bogus.)

5. Nobel Prizes are not the great things they once were. President Obama has one and probably will be getting another one soon for the Iran deal, along with the Ayatollah. Jimmy Carter and Mahmoud Abbas are on the waiting list. Yes, yes, I know this will be Carter’s second one also. He’ll be receiving this one
for not liking Mr. Netayahu.

6. Ah, the mysteries of the brain. It is not for nothing that Alzheimer’s Disease remains a puzzle, while dental science has surged ahead.
stevenz (auckland)
Musings of my own:

President Obama is trying to earn his retrospectively. He won't get a second because the first one hasn't come to full maturity.

Jimmy Carter is a Great Man. If anyone deserves a second peace prize, it's him. (The Mahmoud Abbas thing is a puzzle.)

I couldn't get past algebra. Thus went my dream of being an astronomer.

Could be a nervous habit. (I hadn't noticed it until you pointed it out.)

If a model is tested repeatedly and works it isn't bogus.
SqueakyRat (Providence)
For a self-confessed know-nothing, your "musings" are remarkably presumptuous.
afacio (NYC)
Dr. Nash wasn't an economist and his theory of noncooperative games was written as a mathematical paper to solve a mathematical problem. Whatever you think of economics, it can't be disproven because it's a mathematical fact.
Azim (SJC)
"Dr. Nash was widely regarded as one of the great mathematicians of the 20th century,"
Curious to know why he wasn't regarded as one of the 'greatest'?
srwdm (Boston)
For that you must look to John von Neumann.
SqueakyRat (Providence)
Being one of the great doesn't preclude being one of the greatest. Just saying.
Max (Willimantic, CT)
One who does not perceive the syntactical sense of "one of the great. . ." and the nonsense of "one of the greatest" needs to analyze. Many may be “one of the great”. There cannot be “one of the greatest” because there is only one greatest. The writer's syntax is beyond criticism and syntactically and mathematically correct.
Kathy (California)
John Nash's game theories in economics did not include the mentally ill, those oppressed by poverty. I think he became schizophrenic because he intuitively sensed that his equations were unbalanced because of these omissions. A brilliant mind includes all the variables in the equation. He omitted critical elements. Hence, the mental backpedaling.
Linda (New York)
Yes, it's interesting his work -- as interpreted and over-interpreted in so many fields of study -- presumes rationality, which is so often wrong. It wouldn't account for this tragic car accident, for example.
Merlin (Atlanta)
If Dr. Nash thought his theory was inadequate as you propose, it is more rational based on his personality, that he would work toward a solution rather than relapse into "mental backpedaling". Anyone who understands the construction of theories (in physical and social sciences) knows that theories can be debunked all the time, or may form the foundation of other theories. Nash's theory has done the latter, and it is not necessary for him to feel inadequate. It is also one of the reasons science hardly confers the title "Law" to new theories. Very few theories such as the Law of Gravity are time-tested.

Diagnoses of REASONS for mental illness is extremely difficult, unlike many other diseases. It cannot be simulated in a laboratory. The mind is connected to the workings of the brain, but it is not a physical organ that can be dissected and studied.
CK Johnson (Brooklyn)
Yes, they weren't wearing their seatbelts, but it sounds like it was a horrific crash and one caused by the taxi driver's overly aggressive driving. I always dread getting into one of those cabs out of Newark. They seem so sketchy. Will this terrible loss serve as a call to action for the NJ taxi commission?
Stephen C. Rose (New York City)
One account has the cab being struck by a car that had just passed another vehicle.
VM (New Jersey)
Although of little significance, why do you assume it was a cab out of Newark?
Kestril1 (New Jersey)
They were taking the cab from Newark Airport to their home.
JANIS (PALO ALTO, CA)
Were Dr. Nash and Alicia Nash wearing their seatbelts? It seems not; they were thrown from the cab. A very heavy price to pay for not belting in. Maybe this is their last lesson for the world. Buckle up!
stevenz (auckland)
You just triggered a thought. Are taxi cabs subject to regular safety checks? A kind that would assure that seat belts were functioning and securely anchored.
Susan (Beverly NJ)
My condolences to the family; very sad to have lost two such extraordinary people at once.
Miriam (NYC)
My condolences to the family, but I am outraged that yet again a driver of a car is involved in an crash, gets away relatively unscratched while the passengers are killed. Often these drivers have had their licenses suspended numerous times and at most they'll just get another suspension, if even that. Yes, the Nashes should have been wearing seatbelts, but how many "accidents" have taxi and limo drivers been involved in lately and they aren't even charged with negligence when something like this happens? They jump curbs, run into pedestrians in crosswalks and lose control of their cars on the highway. Perhaps we need more rigorous testing for these drivers and less second chances. As for all drivers, once they have a certain amount of moving violations they should be sent to jail is they are involved in a serious crash and their licenses should be permanently revoked.
ring0 (Somewhere ..Over the Rainbow)
The teaching lesson here is always wear a seat belt in a vehicle, even in a cab.
Laughing Achiever (Boston)
While attending school in western Massachusetts, I was privileged to oversee Dr. Nash as he spoke about his newer theories on eliminating inflation.

Today, with every money hungry investor scrambling to make money before interest rates potentially rise next fall, at cost to the American middle class, on some mathematical level one has to wonder if he had some prophetic intelligence left in his Beautiful Mind.
Carlos Santos (Logan, Utah)
Somebody that has gone to hell and back definitely deserves to be in Heaven... RIP John & Alicia Nash.
Paul King (USA)
A tragic end to two beautiful lives.
Somehow not befitting such an interesting, impactful man.

Forgive me if this seems mundane on comparison to the tragedy.
Maybe the last bit of information we can take from John Nash is to not be a passive rider with all-too-reckless cabbies.
I recall a trip from JFK to Manhattan that was making my hair stand up. I told the driver forcefully to slow down and take it easy or I wouldn't pay him.

I didn't mince words or tone.

He straightened up.

Rest in peace. So sorry to hear this news.
Everyone else take good care.
MC (California)
A Beautiful Life.
RIP.
KZ (Middlesex County, NJ)
I have been in cabs and livery vehicles in which the drivers played with cell phones, talked to dispatchers, drove like maniacs. I don't suppose we know yet what exactly caused this crash, but the Turnpike as a lawless and deadly road, as are most of the major roads in this state. Maybe seat belts would have saved their lives, but maybe not. Let's not blame the victims here. I wonder how many people have to be killed or maimed before road safety is taken seriously here.

What a tragic loss for Princeton and the world.
blasmaic (Washington DC)
The seat belts were there. The driver used his. He survived.

John F. Nash was a genius and he was disabled, but he was also arrogant, selfish, and often just downright mean to others. We have to say nice things because we can't have people who are not talented like John Nash using John Nash as an excuse for their own horrible conduct.

Nash was returning from a European trip where he received an award and one colleague described the trip as "perfect." Could Nash have impulsively caused the crash to end on a high note, even though it would kill his wife and injure the driver? With John Nash, everything was possible.
Bashh (Philly)
I too have read about the meaner side of Nash's personality. It seemed to me that he did come to realize how he had hurt people, publicly admitted it and made amends to some degree at least. Few of us are saints with or without the heartaches and tragedy of a mental illness. The efforts of Nash to admit his faults was for me what showed that he had a beautiful mind as well as a brilliant one.
naro (nyc)
All commercial passanger vehicles should have a written sign in front of the back seat : "WEARING SEAT BELT IS MANDATORY."
I am surprised that no such sign is required now.
tornadoxy (Ohio)
Very simple, just like when I drive my kids. Vehicle doesn't move until belts are buckled. Cabbies should be required to enforce this, and be inspected.
Max (Willimantic, CT)
I am surprised that anyone, driver or passenger, requires a sign to obey the seat belt law and the laws of physics. NJ law requires drivers not to move a vehicle until all humans are belted. A sign is carrying coals to Newcastle. My point: the sign does no buckling. The driver and passengers do the buckling. I have no sign in my vehicle, but I enforce the seat belt law. If you choose not to, a sign will not aid, so what is holding you back?
David (Brooklyn, NY)
Many a rear taxi seat has swallowed my assigned belt buckle, and when I stuck my fingers down to retrieve it... Ewww, the crumbs!
Bill Gilwood (San Dimas, CA)
I grew up in Princeton and walked around town every day. I first saw John Nash in a bank in 1974 in the center of town. Over the next 17 years I'd cross paths with him at least several times a year, and sometimes several times a week. As we passed each other we'd look at each other; I'd look at him and he at me in a glassy-eyed stare. Early on I'd say hi and he'd say nothing, so after a while I'd just politely nod at him but he'd never respond. I noticed over the years though, starting in the late 80's that he seemed more responsive to his surroundings, but still we never spoke. There were a variety of rumors about him, the most credible being that he had done some important work in math or physics, and had descended into mental illness. Neither I nor anyone I knew, knew his name. Then one Sunday evening in the late spring of 1994 while living in Houston, TX, I opened the Books section of the Sunday NYTs. The entire front page was devoted to a mathematician from Princeton who had done great work, lost his mind, recovered and then received (or was about to receive) the Noble Prize, and there across the top front page was his photo. In a shock of recognition I realized that this was my guy and his name was John Nash! He was smiling and looking like a movie star! I shouted in astonishment, "Oh my God!", loudly enough to be heard by my neighbors.
Diane (New York City)
This story reminded me of my own...

I commuted for years from Princeton to Manhattan and had to take the little shuttle train connecting to the main line (known as the 'dinky'). I would often see a strange man with a very, very flat affect, loitering around the Princeton train station.

He did not confront passengers nor was he even remotely aggressive...just a quiet and extremely strange presence. I'll never forget his face which was absolutely expressionless.

I didn't think about him for years until I ran into John Nash's photograph in connection with "A Beautiful Mind". Like the previous writer, I had an "AHA" moment, realizing that a person I had thought of as inconsequential was, in fact, a rare genius. (and more shame on ME).

May his family find peace after this tragedy.
D. (Kirkwood)
That must have been an awesome feeling...like finding a long lost uncle!
Jim Isenberg (Brownsville, Oregon)
During the early 1970s, I used to see John Nash quite a bit in the basement of the newly-built Fine/Jadwin Halls in Princeton. I spoke to him a few times as well. I was a physics major at Princeton, and I often worked quite late in my carrel in Jadwin Hall. The basement walls were all covered in blackboards, and as often as not, those blackboards were covered by hundreds of lines of rather strange free verse. When I first saw the guy writing these lines, I just watched. He didn't seem to mind. After several months, I decided to ask him about it. He didn't open up very much, but he did tell me how grateful he was to have all these blackboards available for his work.

At the time, I didn't know who he was. We heard rumors, but nobody (at least among those I asked) knew anything about him.

Thirty years later, I met John Nash at a party in Princeton. At the time, he was interested in general relativity, which is my field of research. We chatted quite a bit about black holes. I was tempted to ask him about those verses he had written on the Fine/Jadwin blackboards, but decided to leave that alone.
Elissa (NYC)
Lucky you.
Jim Freeman (KSM, British Columbia)
During the mid 1990's, I took a calculus class from Jim Isenberg at the University of Oregon. The only famous mathematician he didn't name-drop was John Nash!
Richard (Santa Barbara, CA)
Cedric Villani in his wonderful memoir, "Birth of a Theorem," devotes Chapter 29 to John Nash. Nash was one of his heroes. He gives a nice, concise review of Nash's work. I am sure many others will note that the Fields Medal is quite different than a high placing in the Putnam Examination. If John Nash had not become ill at his age, it is probably certain that before he was 40 he would have been given the Fields Medal. This is part tragedy about an extremely gifted person who made major discoveries when he was young.
Mr. Robin P Little (Conway, SC)

He was 86 and she was 82. We can hardly say their lives were cut short. This is a sad way to end an eventful, but difficult set of lives. One can only hope that he and his wife may have been spared greater heartache by this unexpected, tragic ending. May he and she rest in peace.
PrairieFlax (Grand Isle, Nebraska)
Why? They seemed to be doing well at the time of the tragic accident. May they both RIP.
Mr. Robin P Little (Conway, SC)

The reason there is still religion is because, ultimately, nobody knows why. Too many 'why questions' will drive a person mad. Nobody knows why such things happen. But we still need to accept that they do happen.
Robert (Philadephia)
We will not see their like again for a long time. John the mathematician and Alicia, the physicist and loyal partner. Rest in peace, John and Alicia.
Hadley (Boston)
What a loss! Sad way to go after such an extraordinary life. My condolences.
sweinst254 (nyc)
As Robin Little correctly noted above, bemoaning the loss and the way to go at 86 may be a bit out of place. It may have saved them both the heartache that comes with losing a spouse and trying to survive very old age in the United States alone.
Dorothy Dundas (Boston)
I hope people are noticing that this man finally went off all medication and returned to an equilibrium. It is a tragedy that he was forced to undergo medication and ECT when simply the passage of time and a gentle environment might have helped him the most.
DJS (New York)
Most people do not recover from schizophrenia with “simple passage of time and a gentle environment.” Dr. Nash did not. It was many decades later when he somehow recovered.
outis (no where)
Thanks for pointing this out.
Kermit Cole (Santa Fe, New Mexico)
He, in fact, attributed his recovery to the fact that he did not take the medication. That, and the support he received. What is also overlooked in the movie, but not in the book, is the extent of the traumatic experiences he endured in childhood and in college. The book does not draw this inference, but the types of trauma he went through must certainly have contributed to his later psychosis.
Richard Scott (California)
One of the greatest minds in mathematics and economics of the 20th century... taken down by an errant taxi cab driver in New Jersey. Perhaps John would appreciate that sort of irony. My son has struggled with schizophrenia for 35 years. Mr Nash's story of struggling back towards dignity is a story my son could relate to. I only wish he could have known that; that I could have told him, or my son.
So it's up to me to say it now: thank you John Nash, for the many ways you contributed to good in this world.
C.Z.X. (East Coast)
Are you aware that Nash's own son has schizophrenia?
outis (no where)
Actually, taken down by the failure to buckle up. But it is possible that the cab did not demand it, offer it because it is not the law for cabs.

This is not good. First Bob Simon and now Dr. Nash and Alicia.
Greg (Montreal)
Kind of sad that you thought it was more important to include a still of Russell Crowe playing John Nash instead of a photo of John and Alicia Nash together.
radha vyas (Pleasanton)
In a reality world of Kims, Bacher_nonsense, Housewives, HoneyBooBoos, and many more trashy stories which are of no use, and the habit of reading good books going down, In a way I am glad that the movie based on the book put Dr Nash put his Beautiful Mind into the foreground, and Yes, NYTimes ought to have published pictures of the couple, Alicia Nash who never left his side to the end.
sweinst254 (nyc)
There's a photo of Nash alone, and many casual readers will relate more closely to his obituary having seen a photograph of the actor portraying him in the film. The film is essentially the reason why his death is being covered so heavily, so deal with it.
Jana Hesser (Providence, RI)
Kali Rynearson (Chicago, IL)
As someone who studied advanced Calculus and algebra in high school, I was familiar with John Nash at a fairly young age. As his Princeton recommendation letter stated, he was a genius: his rare combination of creative and logical skill (or left and right hemisphere specialization in the brain as the biological paradigm in psychology would argue) is unique to the genius mind. This article also compares him to Jane Austen and his work's influence in mathematics to that of DNA sequences in biology. Furthermore, there are pioneers in each field of human knowledge (e.g. history, psychology, the natural sciences, et cetera), and John Nash was arguably a pioneer in mathematics, one of the greatest minds of the 20th century. Future generations of pure mathematicians and economists alike will be influenced by his work, as he was influenced by Riemann's, and he was a game-changer (pun intended). The world lost a great mind today, may he rest in peace.
ring0 (Somewhere ..Over the Rainbow)
So his contributions seem to favor math rather than economics.
Of course the latter discipline is sometimes referred to as "disguised math."
Zeitgeist (<br/>)
You forget the fact that Dr.Nash got his Nobel prize not for his prowess in maths ( no one gives a Nobel for mathematical prowess ) , but for his economic theory ( Game theory ) which he advocated need not be. Zero sum game but could be played beneficial to both the cat as well as the mouse. This unrealistic theory ( especially in economics ) was hoisted so high simply because the predatory ever greedy corporations could keep the mousy consumers of goods hopeful that if you continue spending one day it will benefit you someway , because you are dinned into your heads that its not a zero sum game .

But sadly it has always been a zero sum game in the market place. OT necessarily to start with but cruelly to end with . The profiteers become greedier and greedier as the game proceeds and the losers , the consumers become more and more hopeful which gets increasingly exploited by the ever greedy ever predatory markets . Just human nature .

I don't know which way the game need to be played so that it doesn't become a zero sum game , without the government regulates the markets . But the government , instead let the markets loose freely on the ever hopeful customers . It has now resulted in. Collapse of economy .

But it was not the fault of Dr. Nash who was elevated to nobelhood on the shoulders of his economic theory instead of his mathematics . It is the fault of the greedy corporations and more of the government who failed in their duties to regulate the markets .
Jill Bornd (Canada)
My thoughts and prayers go out to their family, Interesting bio about Alicia Nash here http://dailyentertainmentnews.com/?p=58828 such an amazing woman
L.Tallchief (San Francisco)
Yes, a beautiful and amazing woman.
Suzie Siegel (Tampa, FL)
Thanks for this link! It's a shame that Alicia Nash isn't getting more credit for all than she did to keep him going. We'll never know what she might have accomplished as a physicist if circumstances had been different.
Valerie Jones (Mexico)
It's always the beautiful minds that leave us way too early.

May the Nashes rest in peace together with the comfort and joy of lives well-lived.

I am just so very saddened to read this bit of news today.
Bill (Austin, Texas)
He died at the age of 86.
Kevin Hill (Miami)
He was 86.
Valerie Jones (Mexico)
And 86 is too soon.

Honestly, it's as though some people lie in wait in this forum just to attack. Have you nothing better to do?
LR (NJ)
All the accomplishments and genius exhibited and unfortunately Mr. Nash couldn't buckle a seatbelt while sitting in a taxi on the New Jersey Turnpike. It cost him his life...
ring0 (Somewhere ..Over the Rainbow)
On a quick cost-benefit analysis it may not appear rational to buckle up. When you're 86 you have less to lose.
Zack (Phil PA)
Hear hear.

The obituary might have pointed out that, like the notorious Tracy Morgan NJ Tpk accident, had the Nashes been using their seat belts (taxis do have them) they might have survived.

When taxi's will not drive until the passengers Click It, these sad, unnecessary stories will repeat ad nauseam. Why is it illegal for private cars to be driven without using the installed seat belt, but taxi's are not? "The taxi driver and the driver of the other car were treated for non-life threatening injuries. No criminal charges have been filed. "

At least they weren't in an Uber. Maureen Dowd would have been totally freaked: http://www.nytimes.com/2015/05/24/opinion/sunday/maureen-dowd-driving-ub...
Victor Sasson (Hackensack, N.J.)
Two more prominent people killed riding in a taxi or limousine who may not have been wearing their seat belts. Bob Simon of 60 Minutes was killed after his limo crashed on 12th Avenue in Manhattan, and he wasn't belted in.

There should be a law to require hired drivers to instruct their passengers to put on their seat belts or face liability if they crash and their passengers die.
BlueMoose (Binghamton)
Unfortunately the seat belts in taxicabs and limousines are often filthy and buried in the seat cushions. I think the suggestion that drivers be required to ensure that their passengers are belted is a good one and the condition of those belts should be part of annual inspections.
Elizabeth W. (Croton, NY)
It would be easy. The driver would not start until passengers had fastened their seat belts. That's what I do all the time.
KZ (Middlesex County, NJ)
Just who would enforce such a law in this state? There are plenty of traffic laws here, and most people totally ignore them. Cab drivers are some of the worst offenders. Tailgating is supposed to be a 5-point violation. When did you ever hear of anyone being pulled over for that. I've been tailgated by tractor trailers on the Turnpike and Route 287 so closely that I could clearly read the Peterbilt logo in my rear-view mirror. This tragedy will be forgotten until the next tragedy.
James (Northwest)
Words cannot speak to the enormity of this loss. One did not have to be a theorist or academic to appreciate this man's work. It is truly a loss for our country. My deepest prayers and sympathies to his family and to Dr. Nash, thank you, sir for your work.
American Expat (Vancouver)
Loss to mankind.
Nadia (Dhaka)
I was looking for the lifestory and achievement of John Nash. Finally, I found the details here at http://usanewsbag.blogspot.com/2015/05/john-nash-life-story-achievement-...
Ron Munkacsi (Sneads Ferry NC)
What a great educational talent and a tremendous tragic loss. It was reported that neither the Professor or his wife were wearing seat belts, which are provided in the rear seats of taxis. As a first-responder, we should all be reminded how simple forgetfulness can sometimes yield tragic results. Our prayers for their family.
Valerie (Pleasanton, CA)
Not all taxis have seat belts, which should be required by law. I have refused taxis and limos that did not have seatbelt available.
DJS (New York)
Where was this reported? If the Nash’s were not wearing seat belts, It’s an odd omission on the part of the New York Times
rkbirk (Great Falls, MT)
Beautifully written, Erica Goode.
Nancy (Great Neck)
How saddening.

But I have a question. Is New Jersey an especially dangerous state in which to drive? By anecdote, there do seem to be awful accidents on New Jersey roads.
Lava (New York)
this might be a difficult question for New Yorkers to answer politely
Harvey P (Boynton Beach, Florida)
It is no worse than any other place. For really scary driving try southern Florida!
LT (New York, NY)
New Jersey has more people and cars per square mile than any other state--although its nickname is "The Garden State." That of course may lead to more auto accidents. And of course, because it is a gateway to New York and New England, the turnpike is the most heavily traveled one in the U.S.
meh (Sullivan County, NY)
It would have been nice if there were some notice here of Mrs. Nash's life--unless the Times is going to give her her own obituary?
G. Morris (NY and NJ)
May I second that suggestion.
Caro (Hoboken)
I agree. I was curious to read more about her.
MEP (Michigan)
It is a rare woman to divorce and then care enough to take care of him when he needed it the most. The norm is to take while taking is good and desert him when there is nothing left. She should be remembered as the one with the beautiful heart. Both will be missed.