Freeman Dyson — the world-renowned mathematical physicist who helped found quantum electrodynamics with the bongo-playing, Nobel Prize-winning physicist Richard Feynman and others, devised numerous mathematical techniques, led the team that designed a low-power nuclear reactor that produces medical isotopes for research hospitals, dreamed of exploring the solar system in spaceships propelled by nuclear bombs, wrote technical and popular science books, penned dozens of reviews for The New York Review of Books, and turned 90 in December — is pondering a new math problem.

“There’s a class of problem that Freeman just lights up on,” said the physicist and computational biologist William Press, a longtime colleague and friend. “It has to be unsolved and well-posed and have something in it that admits to his particular kind of genius.” That genius, he said, represents a kind of “ingenuity and a spark” that most physicists lack: “The ability to see further in the mathematical world of concepts and instantly grasp a path to the distant horizon that’s the solution.”

Press said he’s posed a number of problems to Dyson that didn’t “measure up.” Months and years went by, with no response. But when Press asked a question about the “iterated prisoner’s dilemma,” a variation of the classic game theory scenario pitting cooperation against betrayal, Dyson replied the next day. “It probably only took him a minute to grasp the solution,” Press said, “and half an hour to write it out.”

Together, they published a much-cited 2012 paper in the Proceedings of the National Academy of Sciences.

The next year, Press traveled to Princeton, N.J., for a two-day celebration of Dyson at the Institute for Advanced Study, Dyson’s intellectual home for the past six decades. In honor of Dyson’s 90th birthday, there was seemingly boundless cake, a forest of long, white candles, 350 guests — including his 16 grandchildren — and lectures recognizing his eclectic achievements in math, physics, astronomy and public affairs. H. T. Yau of Harvard University commenced the math section, launching into Dyson’s work on the universality of random matrices. George Andrews of Pennsylvania State University and Kathrin Bringmann of the University of Cologne followed with the implications of Dyson’s early contributions to number theory, which he began contemplating in high school. William Happer, a physicist at Princeton University and a fellow skeptic of the perils of anthropogenic climate change, closed day one with a talk provocatively titled “Why Has Global Warming Paused?”

Dyson admits to being controversial when it comes to climate science. But during an hour-long interview with Quanta Magazine in December, he said: “Generally speaking, I’m much more of a conformist.” Still, he has written fondly of science as an act of rebellion. In his 2006 anthology of essays and reviews, “The Scientist as Rebel,” Dyson writes, “I was lucky to be introduced to science at school as a subversive activity of the younger boys.” With characteristic concern for social issues, he goes on to advise parents: “We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice.”

On the second day of the 2013 celebration in Princeton, after numerous speakers had recounted past collaborations with Dyson, alternately feting and roasting his brilliance, Press took a different tack. Referring to their collaboration on the prisoner’s dilemma, Press — a professor at the University of Texas, Austin — said he “thought it would be a little extreme to reminisce with Freeman about a paper that was just published.” Instead, he described his own recent result on safer “adaptive” clinical trials, adding that although he had solid computational data, the mathematical analysis proved too formidable. “I wish I had worked on it with Freeman — and maybe still will get the chance to do so,” he said slyly.

Press’ comment proved prescient. After the celebration, Dyson began mulling over the problem — unbeknownst to Press, who didn’t find out until Quanta contacted him in March about the new “collaboration.” “I’m glad to know it’s on his stack of things to do!” he said. “I’m looking forward to seeing what he comes up with.”

Quanta Magazine interviewed Dyson at the institute, just days after his 90th birthday. An edited and condensed version of the conversation follows.

QUANTA MAGAZINE: Technically, you retired from the Institute for Advanced Study 20 years ago. What are you working on now?

FREEMAN DYSON: I used to be a scientist and did a lot of calculations. It was a competitive world, and when I got older, I decided I wouldn’t compete with the bright, young people anymore, so I write books instead. And now I’ve become a book reviewer for The New York Review of Books. About once a month, I write a review, and then I get a lot of response and correspondence, people who are finding things I said which aren’t true.

What did you do prior to writing book reviews?

I was trained as a mathematician, and I remain a mathematician. That’s really my skill, just doing calculations and applying mathematics to all kinds of problems, and that led me into physics first and also other fields, such as engineering and even a bit of biology, sometimes a little bit of chemistry. Mathematics applies to all kinds of things. That’s one of the joys of being a mathematician.

Why math?

I think the decisive moment was reading the book “Men of Mathematics” by Eric Temple Bell. Bell was a professor at Caltech, and he wrote this book, which is actually just a wonderful collection of biographies of mathematicians. Historians condemn it as romanticized. But what was wonderful about this book is that he showed the mathematicians as being mostly crooks and people of very mixed kinds of qualities, not at all saints, and many of them quite unscrupulous and not very clever, and still they managed to do great mathematics. So it told a kid that “if they can do it, why can’t you?”

What are some of the big questions that have guided your career?

I’m not a person for big questions. I look for puzzles. I look for interesting problems that I can solve. I don’t care whether they’re important or not, and so I’m definitely not obsessed with solving some big mystery. That’s not my style.

What kinds of puzzles first intrigued you?

I started out as a pure mathematician and found problems that just arise out of the very nature of numbers, which are amazingly subtle and difficult and beautiful. That was when I was about 17 or so, just at the end of high school. I was interested in numbers before I was interested in the real world.

What is it about numbers that made you want to figure them out?

It’s just like asking, “Why does a violinist like to play the violin?” I had this skill with mathematical tools, and I played these tools as well as I could just because it was beautiful, rather in the same way a musician plays the violin, not expecting to change the world but just because he loves the instrument.

You’re known for your work in quantum electrodynamics — which describes interactions between light, matter and charged particles — and in solving the renormalization problem — which helped rid the mathematics of unwanted infinities. How did that work come about?

When I arrived in Cornell in 1947, there just had been done a beautiful experiment at Columbia on the hydrogen atom. The hydrogen atom is the simplest atom, and you ought to be able to understand it if you understand atoms at all. So, these experiments were done by Willis Lamb and his student Robert Retherford at Columbia, observing for the first time the very fine behavior of hydrogen using microwaves to examine the hydrogen atoms, and Lamb got very precise results. The problem was the quantum theory wasn’t good enough to explain his results. Dick Feynman, who was an absolute genius, had understood more or less how to explain it but couldn’t translate his ideas into ordinary mathematics. I came along and had the mathematical skill, making it possible to calculate precisely what the hydrogen atom was doing, and the amazing thing was that my calculations all agreed with the experiment, so it turns out the theory was right.

I didn’t invent anything new — I translated Feynman’s ideas into mathematics so it became more accessible to the world, and, as a result, I became famous, but it all happened within about six months.

Did it lead to other questions that you wanted to explore?

I got job offers from everywhere in America and also in England, but the problem was that I didn’t actually want to settle down yet and become an overburdened professor with lots of students. So I escaped to England and had two happy years at Birmingham without any responsibilities and continued working on other problems.

I was very much interested in space travel, and so the next exciting thing I did was to work with a company in California called General Atomics for a couple of years building a spaceship. In those days, people were willing to take all kinds of risks, and all kinds of crazy schemes got supported. So there was this bunch of crazy, young people — the leader was Freddie de Hoffmann, who had been at Los Alamos [National Laboratory] and knew all about nuclear bombs — and we decided we would go around the solar system with a spaceship driven by nuclear bombs. We would launch the ship into space — “bomb, bomb, bomb, bomb,” about four bombs per second — going up all the way to Mars and then afterwards to Jupiter and Saturn, and we intended to go ourselves.

What happened to Project Orion?

I spent two wonderful years in San Diego having grand dreams of spaceships. We not only did calculations, we also flew little models about a meter in diameter with chemical explosives, which actually went “bomb, bomb, bomb, bomb” a few times a few hundred feet up. It was amazing we never got hurt. I think we didn’t even have to buy the explosives. We had some Navy friend who stole it from the Navy. Anyhow, we certainly borrowed the test stand from the Navy where we did these little flight tests. That lasted for two years. By that time, it was clear that the competition was actually going to win, the competition being Wernher von Braun and the Apollo program, which was going to go with ordinary rockets to the moon.

The Orion spaceship sounds like something a child might dream up. How disappointed were you that this “grand dream” wasn’t realized?

Of course we were very disappointed when it turned out that the Orion never flew, but it was clear that it would make a horrible mess of the landscape. These bombs were producing radioactive fallout as they went up through the atmosphere, and although at that time we were exploding bombs in the atmosphere for military purposes, which were much bigger than the ones we proposed to use, still we would have made a contribution to the general contamination, and that was the reason why the project failed, and I think it was a good reason.

You’ve developed a reputation as a maverick scientist with contrarian views. Where do you think that comes from?

I think the notion that I always like to oppose the consensus in science is totally wrong. The fact is there’s only one subject that I’ve been controversial, which is climate. I spend maybe 1 percent of my time on climate, and that’s the only field in which I’m opposed to the majority. Generally speaking, I’m much more of a conformist, but it happens I have strong views about climate because I think the majority is badly wrong, and you have to make sure if the majority is saying something that they’re not talking nonsense.

With a majority of scientists on the other side of this issue, what would it take to convince you to switch sides?

What I’m convinced of is that we don’t understand climate, and so that’s sort of a neutral position. I’m not saying the majority is necessarily wrong. I’m saying that they don’t understand what they’re seeing. It will take a lot of very hard work before that question is settled, so I shall remain neutral until something very different happens.

You became a professor at Cornell without ever having received a Ph.D. You seem almost proud of that fact.

Oh, yes. I’m very proud of not having a Ph.D. I think the Ph.D. system is an abomination. It was invented as a system for educating German professors in the 19th century, and it works well under those conditions. It’s good for a very small number of people who are going to spend their lives being professors. But it has become now a kind of union card that you have to have in order to have a job, whether it’s being a professor or other things, and it’s quite inappropriate for that. It forces people to waste years and years of their lives sort of pretending to do research for which they’re not at all well-suited. In the end, they have this piece of paper which says they’re qualified, but it really doesn’t mean anything. The Ph.D. takes far too long and discourages women from becoming scientists, which I consider a great tragedy. So I have opposed it all my life without any success at all.

How is it that you were able to escape that requirement?

I was lucky because I got educated in World War II and everything was screwed up so that I could get through without a Ph.D. and finish up as a professor. Now that’s quite impossible. So, I’m very proud that I don’t have a Ph.D. and I raised six children and none of them has a Ph.D., so that’s my contribution.

Looking back at your career, how has your approach to science changed over the decades?

I’ve now been active for something like 70 years, and still I use the same mathematics. I think the main thing that’s changed as a result of computers is the magnitude of databases. We now have these huge amounts of data and very little understanding. So what we have now — I forget who it was who said this — are small islands of understanding in a sea of information. The problem is to enlarge the islands of understanding.

What scientific advance do you see on the horizon that will have a big impact on society?

People are often asking me what’s going to happen next in science that’s important, and of course, the whole point is that if it’s important, it’s something we didn’t expect. All the really important things come as a big surprise. There are many examples of this, of course, dark energy being the latest example. Anything I mention will be something that, obviously, is not a surprise.

Are you currently working on a math problem?

The question of what I do with my time is a delicate one. I’m not really doing science competitively, but I like to have a problem to work on. I’m very lucky to have a friend, Bill Press, who is an expert on clinical trials, which actually turns out to be an interesting mathematical problem.

He published a paper explaining how to do clinical trials in a really effective way with a minimum loss of life. He’s a computer expert, so everything he does is worked out just with numbers, and so I have taken on as my next task to translate what he did into equations, the same way I did with Feynman. I’m not sure whether it will work, but that’s what I’m thinking about at the moment.

What does it mean for someone with so many intellectual pursuits to be retired?

When I retired as a professor of the institute, I kept all the privileges. The only thing that changed is the paychecks stopped coming. I still have an office and all the secretarial help I need, plus a place at the lunch table. One more advantage is not having to go to faculty meetings.

This article was reprinted on Wired.com.