On May 19, 2015, Nobel laureate John Forbes Nash received the Abel Prize together with his former mentor, Louis Nuremberg, at an awards ceremony in Oslo's University Aule from the hands of King Harald for his outstanding scientific achievement in the field of mathematics.

The ceremony was followed by a reception and a public interview with the Abel Laureates and by a dinner at the Norwegian King's castle in the heart of Oslo.

On the following day, Nash arrived at the University of Oslo to give his prize lecture in front of an international audience of scientists and students.

It would be his last lecture. He was not a normal human being. He was pathologically logical.

Nash was exposed to army, game theory. Maybe he had left the real world before anybody knew it. He liked partying. He liked good times.

Are you a communist? I was always a concern. Who is wasting your time today?

A boy is born in Bluefield, West Virginia. He's named John Nash, just like his father, who's an electrical engineer, more on the scientific side of his job. His mother is a language teacher at a public school.

The boy has absolutely no interest in sports, movies, or even being a boy scout. In grade school, right after kindergarten, the kids are asked to write down numbers. Nash remembers. Students were taught to do some calculations, addition and multiplication, subtraction, and to write numbers down in standard digital notation.

And so I did numbers with larger number digits. Teachers get interested in the boy who dreams himself away from football games and parties.

His mother encourages this, and his father gives him some books about famous mathematicians. Nash gets lost in the biographies of mathematicians, participates in math competitions, loses, comes back stronger, and wins. Now he has offers from MIT, Harvard, and Princeton, but picks Princeton for a scholarship he's been offered.

He is a strange young man, doesn't look you in the eyes while talking, doesn't answer questions when he thinks they're not good enough, and loves playing pranks on the people he works with.

Is it arrogance or a kind of social incompetence? No matter what, the others have come here to study. Nash has come to build his own theories. He's here to win. All the students who were admitted received a grade of A in all their courses every year.

It was a big room, and it had maybe 15 students and 10 professors, and they were always all there in this big room. If you had a question, you could ask them, and if it were physics, you could ask Einstein, but I couldn't understand his accent very well.

Von Neumann was perfect. John Nash was there, and he was super logical.

He was a jolly young man. He was very, very bright, very bright. In addition to his work in game theory, he afterwards did some very important work in pure mathematics.

A little bit brash, unexpected. He liked partying, he liked good times. We spent quite a bit of time together. Here you have a man that you can consider a genius who, unlike most great American mathematicians, is a real American in some sense.

I mean American for many generations. In his parents, no particular predisposition for mathematical research, so Guy really out of nowhere in a sense.

But also meeting an extremely favorable environment, going to New York in a situation that was just after the Second World War, in which America was filled with great scientists, great mathematicians who had emigrated from Europe because of the war.

There were Jewish mathematicians, but also all their friends, and there was an ecosystem really buzzing with great ideas. And also, the Second World War is the moment in which pure and applied mathematics meet in the United States with great consequences. And Nash was exposed to problems related to army, game theory, very applied problems, at the same time as he was exposed to rather pure ideas.

He got to work on partial differential equations, subject which was very applied compared to what was the talk of everybody in France about the same time,

when it was very much influenced by very abstract movements like Boba-Kee. So the situation of Nash is that of a real genius meeting a very favorable ecosystem. When I knew him, it was at Princeton. I don't remember going to any classes because all

of the faculty and the good students were in this one big room most of the time. It was a community. It was just the place, the only place to be. If you went anywhere else, you would miss something.

Well, first of all, I should say that I think Nash is responsible for bringing me into game theory. We got a problem from Bell Telephone Laboratories, who were developing a ground-to-air missile.

And we were given this problem to analyze. And I realized that the problem had to do with game theory.

I remember the conversations with Nash, and I realized that it had to do with game theory. And from the analysis of this problem, I became interested in game theory itself. Nash developed, I think, two fundamental concepts in game theory.

One is in the theory of strategic games, this equilibrium concept. And one is in the theory of cooperative games or coalitional games, his bargaining solution.

And these are two different concepts entirely. And both had a tremendous impact on my work, as they did on all of game theory.

I would never have thought of that. That was my impression of Nash. He had ideas that I would never have thought of. I really thought he was a genius. It is famous that the Romanian embedding was asked him as a kind of joke by one of his colleagues,

who was really annoyed at the behavior of Nash, that he found too much arrogant. And behind this appearance of arrogance, it is clear also, I think, that Nash felt very insecure

and needed to be very much reassured about his capacity. The work on bargaining was very instrumental in my work in developing the theory of what are called NTU games, non-transferable utility games.

Nash is most famous in general for his work in equilibria, game theory. But when you start reading the work that he did, say between 1954 and 1958, a short period of time on problems of the Romanian embedding and the problem of regularity of solutions of partial differential equations,

it is just magical, because these papers are so full of ideas, full of concepts, full of techniques, they are extremely rich.

They are somehow a bit messy, especially the first versions of the smooth embedding theorem, it is known as especially messy. But the non-smooth embedding theorem, the first one of the series, is crystal clear, almost crystal clear. And also some of the ideas in the regularity work are beautifully explained.

These are really revolutionary works, and when you read the papers even nowadays, you feel something very special about these papers. Nash's work from that period contains to an extreme degree two of the most important characteristics in the art of mathematics.

One is the element of surprise, and the technique which Nash used to solve the problem of Romanian embedding, nobody expected. It gave rise to the convex integration, it gave rise to the Nash-Moser technique, it was really like out of the box.

And the other thing is the idea of combining parts coming from various points of view. You know it's like the conductor explaining the part to each of the instruments in the orchestra.

Could you do something? And none of the instruments has any idea of what is the complete orchestration, how it feels. Then everybody plays together and you hear the symphony. Nash at the time was at the top of his game. His unconventional methods and ideas had made him a symbol of the new spirit in mathematics.

In 1955 he became friends with one of his students, Alicia Lardet. Nash married Alicia in February 1957, and by the autumn of 1958 they are expecting a child.

Nash continued developing his work on the embedding problem for Romanian manifolds, published in 1956. This paper contains his famous deep implicit function theorem. After this he worked on ideas that would appear in his paper, Continuities in Solutions of Parabolic and Elliptic Equations, which was published in the American Journal of Mathematics in 1958.

He was clearly going for a Fields Medal. Other mathematicians found a different proof of the same result, not as rich as the proof using the baby Nash-Moser technique, but much simpler. And about the other paper about the regularity, that paper appeared exactly at the same time as the paper by Ennio de Giorgi.

And somehow the method of de Giorgi gained more recognition among specialists of partial differential equations. But it is clear that at the time John Nash had done more than enough to deserve a Fields Medal.

And Nash himself attributed the fact that he did not get it to the concomitants of his proof and the proof by de Giorgi, and it may very well be the case.

These are accidents, you know. Nash was very young at the time. It is clear that he would have got the Fields Medal. I think it is clear he would have got the Fields Medal four years after Tom got it. But we know that tragically he had these problems of mental illness,

which stepped in and prevented him to remain active in the community of mathematicians. I sent letters to the NSA, which is this organization that is causing anger around the world by listening to the conversations of Merkel,

which you thought was private. The game is they don't want it to be understood where their position is in terms of cryptological competence. A couple of months later, Nash's colleagues realized he was acting strange.

What was the first sign that Nash was in serious trouble? The fact that he didn't come to class. I taught his class a few times. He started to talk in a more dreamy way.

He did see significance in numerical events. I don't think I could tell when he was choking or entangled in some terrible fantasy. On January 4, 1959, he started his game theory course to the class saying,

The question occurs to me, why are you all here? One student immediately dropped the course. Nash asked a graduate student to take over and vanished for a couple of weeks. When he returned, he walked into the common room with a copy of the New York Times saying that it contained encrypted messages from outer space.

Was this a joke? Norbert Wiener was one of the first to recognize that Nash's extreme eccentricities were actually symptoms of a medical disorder.

After months of bizarre behavior, Alicia had her husband involuntarily hospitalized at a private psychiatric hospital outside of Boston. Upon his release, Nash abruptly resigned from MIT, cashed in his pension, and went to Europe where he wanted to renounce his U.S. citizenship.

Alicia left her newborn son with her mother and followed Nash who was by then obviously sick and confused. She had Nash deported back to the U.S. I certainly was quite close to Nash when we were both in school and for a few years thereafter. But I must admit, when he had his breakdown, it became very difficult and I was very impatient with him.

I'm sure other people did much more to help him. The people of Princeton were really marvelous in making a place for him. He was in very bad shape many years when he was just not himself.

It was a very hard time. He was committed to mental hospitals against his will a number of times and hated it. His conversation was pretty incoherent. It was amazing when he eventually came back to being himself, but it was very late.

And Alicia was marvelous, I mean, sticking with him through all of this. The following years, Nash spent in hospitals in Trenton and Boston partly in dangerous insulin coma treatment.

Every time he got out, he spent most of his time hanging around at the Princeton campus. His worsening condition depressed Alicia more and more. In 1962, the Nashs got divorced. In 1970, he stops taking pills. The voices that he hears are still there, but he's policing them now.

You see, the medicine doesn't stimulate. It's not like coffee or something. It stimulates the brain. It rather depresses the brain. It reduces the quantity of activity. I give a speech, my last speech to mental health people,

was a meeting of the American Psychiatric Association. I had a text that had a sort of economic view of mental illness. The mind, which does some of the work of that, it may go on strike, and the person doesn't think well because the mind is on strike.

Perhaps if the later conditions were changed for that mind, maybe it would cease to be on strike, except the environment.

The overshadowing question remains. Will he still have great ideas when he returns to reality of the here and now? He tries anyway.

Alicia takes him back as a boarder, and year after year, he's more successful. He gets an office in Fine Hall at the university. He has a house now with Alicia and his son Johnny, who is schizophrenic, too, and a mathematician like himself. In the early 90s, he makes a recovery from his disease.

He says, I would not treat myself as recovered if I could not produce good things in my work. On the campus, there are subtle investigations by people from Sweden, followed by the question, would Nash be able to receive the Nobel Prize for Economics, together with his colleague Reinhard Selden and John Harzani?

I'd like to say something else. I don't know how to describe it, but the most important thing in this video is that it was Shepley and Auman. They were very good people,

and I'd like to say that this is one of them. That's John Nash. Your analysis of equilibrium in non-cooperative games and all your other contributions to game theory have had a profound effect on the way economic theory has developed in the last two decades.

He just wrote two or three papers all together on game theory, but they are what form the foundations of game theory to this day, which is like 60 years later. Nash has a well-respected life in Princeton now. Neighbors and friends, among them mathematicians,

like the man who rarely leaves his house without an umbrella, because a day without rain is just one of two possibilities for him. No matter whether he studies the menu in a restaurant or planning a trip, his main concern is always, what are the options?

He's a welcome guest now to a lot of functions all over the world, traveling restlessly like an ambassador for mathematics. He explains the great progress that could be made through game theory, in economy, in traffic flow, or even in the bargaining solutions of a peace treaty.

His wife Alicia is always at his side. She has sacrificed her own mathematical career to be with him, and they marry a second time in 2001. She is just a large part of my faith.

We are who we are now, and we have a history of it. One of the most brilliant minds of his generation. Ron Howard shoots a biopic on Nash's life called A Beautiful Mind, starring Russell Crowe as Nash and Jennifer Connelly as Alicia.

The film receives four Academy Awards that year. Perhaps it is good to have a beautiful mind, but an even greater gift is to discover a beautiful heart. A beautiful mind. Nash is one of the very few living scientists who were the hero of a Hollywood movie,

and a movie which was really successful. I think there would still be another movie to be made on John Nash, a movie that focuses on the way he works, the way he arrives at his beautiful proofs, and the collaborative work that leads to it.

Back in his office at Princeton University, Nash is inundated with papers from students hoping for advice. He's buried under stacks of papers that he cannot always read or answer. I haven't handled everything perfectly.

Princeton is still the hotbed for many great ideas in math. The common room of the golden years of Princeton is now the cafeteria in Fine Hall, where Nash visits several times a week.

He eyes the mile-long equations on the blackboard, sometimes discussing them with the young mathematicians. Like Marvin Minsky said, he always has that idea that makes the difference. Sometimes it's just a tiny remark that changes the perspective. In any case, Nash's remarks are always fresh and new.

I have an idea relating to space-time, something that might be relevant. I don't have a complete theory. I discovered a partial differential equation, or system, that looks interesting in relation to space-time.

But if it is good, that means that there's something oversimplified about the equations that I'm studying. But it's an approximate.

Things can be approximately correct, and then later on you have to get more complicated. The most overlooked fact of Nash's life seems to be what a warm and helpful person was hidden underneath his shy and demanding personality.

We flew back together, he and his wife and I. They had changed our flight, and so there was nobody to meet him or to meet me. I managed to contact my daughter, who came and picked me up. We chatted for an hour at the airport.

And then when my daughter came, they said, well, they'll take a taxi. And then the horrible tragedy. May 23rd, 2015. John and Alicia Nash die in a car accident on their way back from Oslo's Abel Prize. Their taxi crashes into the guardrail of the Jersey Turnpike near Monroe.

People at Princeton were in a state of shock. A deep sadness could be felt in the community of scientists all over the world.

Some things in the life of a mathematician are barely understandable to the rest of us. There is, of course, the enormous potential in fantasy and abstraction. And then the impressive drama of a life as a mathematician. You spend a good part of your younger years developing your theory. And then it can take the rest of your life for you to prove it.

Nash, though, leaves a whole toolbox of theories and proof behind. And only time will tell which of his legacy works will be picked up by a young mathematician one fine day.

We're going back to the U.S. on the airplane tomorrow.

We might die together. That's fate.