HARI SREENIVASAN: Returning now to the death of Nobel Prize-winning mathematician John Nash.

I'm joined by Nash's colleague and friend Robbert Dijkgraaf, director of the Institute for Advanced Study in Princeton, New Jersey.

So, first off, my condolences to you.

What are you going to miss most about your colleague and friend?

ROBBERT DIJKGRAAF, Director, Institute for Advanced Study: Well, John Nash was such a presence here in Princeton. It is a relatively small community.

And he was a genius of a different kind, somebody who totally transformed mathematics, but perhaps, most important, he was such a gentle and modest man, a great inspiration, I think, for all mathematicians, scientists and human beings.

HARI SREENIVASAN: What was it about his genius that inspired generations of mathematicians? What made him him?

ROBBERT DIJKGRAAF: Well, I think many scientists and mathematicians, they try to kind of climb a mountain that is somewhere out there, and there is a path, although it might be very difficult.

John Nash was a mathematician who just picked his own mountains, and produced results that nobody expected, that actually many people thought were impossible. And, in that sense, he opened up entirely new worlds.

It could have been in economics. It could have been in very abstract mathematics and geometry. He really kind of touched so many different fields.

HARI SREENIVASAN: So, help somebody in the television audience understand kind of the long-term impact of John Nash's work on game theory or how we live our lives today.

ROBBERT DIJKGRAAF: So, John Nash basically proved that, if you have a complicated game, as complicated as it can be, with many players with very different strategies, there is always kind of an optimal form, where, basically, everybody gets the result as best as they can get.

And, actually, this is very interesting mathematically that it exists, but it is used everywhere.

It is used when there are large auctions, whether it is selling goods or it's selling bandwidth. It is basically underlying all of mathematical, economical theory at this moment.

And it is kind of amazing that somebody who had a pure mathematical mind was able to solve this problem that had such an enormous impacts on our lives.

HARI SREENIVASAN: Now, people who have seen “A Beautiful Mind” or ever even haggled for a price understand his impact on game theory, kind of mathematizing our decision-making, right?

But he was actually on his way back during this accident from an even bigger mathematical prize. So, he was still accomplishing feats that most of us have never heard about.

ROBBERT DIJKGRAAF: Yes.

As it's said, he was the only mathematician to win the Nobel Prize. He just won the Abel Prize, which is really an award that recognizes full oeuvre.

And I think it is very important to realize that he was a very broad mathematician, who had this kind of unique ability to touch both our ordinary lives through his work in game theory.

But, also, address very, very deep mathematical problems, thinking about spaces in arbitrary number of dimensions, thinking about the equations, very difficult differential equations that also govern a large part of our world.

HARI SREENIVASAN: Mm-hmm.

ROBBERT DIJKGRAAF: He had — in that sense, I think that the recognition of his almost universal mathematical talent came at this moment is — however unfortunate his passing is, I am very happy that he got his recognition as one of the greatest mathematicians of our time.

HARI SREENIVASAN: And there's also, near the end of his life, his advocacy on behalf of mental illness, which I think will be part of his legacy.

ROBBERT DIJKGRAAF: Yes. And it's such an uplifting story.

We here in Princeton, we have seen him, of course, through many decades and also in his difficult periods. And he was always around.

And the fact that somebody who kind of pushes his own intellect so far, perhaps further than anybody could possibly go, and then kind of climbs back and recovers, and it is really kind of a Greek drama, but it is also a very uplifting story.

And I think, actually, their work for mental health will be recognized and will be remembered and is a great inspiration to many of us.

HARI SREENIVASAN: All right, Robbert Dijkgraaf from the Institute for Advanced Study at Princeton, thanks so much for joining us.

ROBBERT DIJKGRAAF: Thank you.