Image Credits: Nobel Media AB. Photo: A. Mahmoud

We were lucky enough to have an interview with Professor John Michael Kosterlitz, a world-renowned physicist who won the Noble Prize in 2016 for his work on condensed matter physics. Having studied at the Universities of Cambridge and Oxford, he is currently a Professor of Physics at Brown University. The first section of this interview is about his personal experience with physics and academia.

Jonathan: To start off, what would you say attracts you to physics so much?

Kosterlitz: I love problems. I like physics because there are so many unsolved problems and no matter how much you learn, there’s always something new and something you don’t understand. So, I do enjoy trying to solve puzzles. I’m no good at things like crosswords, but I do love physics problems. The thing is that it’s a field which I actually enjoy, because when your doing research, you sort of walk into the unknown and there are no guideposts. So you are on your own and it’s very easy to embarrass yourself and fail. This is something one has to get used to because my career as well as that of other theoretical physicists is 90% failure and 10% success, but that 10% makes up for everything else.

Maxwell: What would you say are some of the hardest puzzles or challenges that you’ve faced in physics and have been able to overcome?

Kosterlitz: That’s very difficult to say because as I said, being a physicist, 90% of my career it has been frustration and failure because the problems are so hard. You start thinking about something that’s not understood and there’s a reason it’s not understood – because there are lots of very smart people in the field who have looked into the problem before and fail. It needs somebody, if you like, out of left field and looking at the problem in a different way. That involves a lot of luck, some smarts, but mostly luck – being in the right place at the right time doing the right problem and being lucky enough to find a way to do it.

Jonathan: How has that been for you in your specific field and your Nobel Prize work as well?

Kosterlitz: The problem that I solved with David Thoules back when we started looking at it in the 1970s was a strange problem because it had never been understood or solved and there was a definite contradiction between existing theory and experiment. Existing theory made a peculiar statement, saying there is no long range order in a two-dimensional system with continuous symmetry. It is certainly a mathematically rigorous theorem and you might ask why was this a problem? Then there was this Russia school (Lev Landau and so on) who made the statement that the low-temperature phase of a system has what is called ‘long-range order’, like a magnetic system where there are lots of little atomic magnets that are pointing in any direction, so the average magnetisation is zero. Then when you cool it down at some critical temperature, these little magnetic moments start lining up – pointing in the same direction so that there is a macroscopic magnetisation. This is very standard in three dimensions, it is well-known and has been observed. So what seemed to be common to all phase transitions known at that time was that a low-temperature phase had long-range order and a high-temperature phase did not, so that was the essential distinction between them. But in two-dimensions (like with thin helium films), there was this mathematical theorem that said there is no long-range order in any non-zero temperature. The natural conclusion from this is that there could be no phase transition because an ordered phase required long-range order. Therefore since there’s no long-range order in such a system, there could be no phase transition – sounded reasonable. But then there was some experiments which showed unambiguously that there were very thin films which were two-dimensional, and the experiment showed that this film had a phase transition to an ordered phase, but this ordered phase could not have long-range order. So there was this conflict between observation and existing theory. So, when there’s conflict between theory and experiment, one should always go with experiment because one can always make mistakes with theory. So this was a puzzle which needed explanation. So to try and resolve this conflict between theory and experiment, it needed explanation, and that is the problem that David Thoules and I looked at and we eventually managed to solve it. Basically, the ultimate solution ended up being semi-rigorous, and so we showed that this system, despite what the old theory said, did have a phase transition, but the low-temperature phase did not have this long-range order and so this was the basic content of why we got the Nobel Prize.

Jonathan: Just to follow up on that, you talk about the clash between experiment and theory. Do you find that scientists are often unwilling to give up their theories when they find a clash?

Kosterlitz: Sure, because if you can’t understand why a system is doing what it does, the natural thing to try is to try and force it into existing theory, because the theory exists, a lot of smart people have worked on it and it’s difficult to think in different ways to conventional theory. Basically, there are two ways you can do this: either one is so ignorant that you don’t know the problem can’t be solved so you try to solve it anyway and that’s what happened. I came to this problem from high-energy physics and particle physics. I got fed up with particle physics, so I went around the department at Birmingham asking everybody I could find if they had a problem I could look at. The standard answer was “no” until I got to David Thoules’ office. I stood there listening to him pontificating and writing equations on the board, not really understanding a thing. Eventually after half an hour I got so desperate and realised I had to do something because I was completely lost, and so I eventually plucked up the courage and asked him “Can you please explain to me David where that first equation came from”. So he turned to me and said “Didn’t I tell you that?” and I could honestly say “No you didn’t” and so he gave me a very clear explanation. From that point on, we got on really well together because that experience overcame my fear of asking him stupid questions. You see, David Thoules was one must term a genius. His mind operated on a different level to almost everyone else, and so compared to David, everyone else was a fool. There was a saying that went round in the department that Thoules was a difficult person to talk to because he didn’t suffer fools gladly and he got impatient. But the trouble was that everyone else compared to him was indeed a fool, and so he was terrifying to talk to or go and ask questions because David knew everything about everything and he was so smart that his reasoning was simply operating at a higher level than that of almost everyone else. So when you talked to him, you felt like a fool because compared to him, you were a fool. So going to approach him with a question was very nerve-wracking because you knew that the answer you would get would probably make you feel stupid. But somehow, this experience of him making a mistake, I thought if we talked a lot in the future, everytime I asked what I thought was probably going to be a stupid question, if I failed to understand, I would just he just hadn’t explained something. This worked well and from that point on, we got along very well together. So it was a pleasure and a privilege to work with a mind like David and so I really started to enjoy doing this style of physics.

Aarit: When I was looking at your work, I noticed that the work on the KT Transitions involved a lot of maths in a range of fields such as statistics and topology. So it’s very clear that maths and physics are very closely intertwined – for example many people call maths the language of physics. Given this is the case, if someone wants to become a physicist, do you think they should opt to do a maths or physics degree at university?

Kosterlitz: Let’s put it this way – mathematics is a language. Once you’ve got some mathematical structure, in principal, all the questions and all the answers are contained in this mathematics structure. Fortunately, in a lot of physics, the mathematical structures work appropriately with the physics. Physics follows these mathematical structures, but it doesn’t have to in the sense that this mathematical structure is an invention that humans have constructed and it may or may not be a suitable language to describe the processes you’re trying to describe. It just turns out that the mathematics we know works to a very great degree. For example, things like calculus were actually invented to describe some physical observations. So, mathematics is just a tool which happens to work. Physicists are supposed to describe the real world and the real world does it’s own thing – it doesn’t care about your mathematics, my mathematics or anybody else’s mathematics. It does it’s own thing. It just so happens that the mathematical structures we work with do happen to work for physics. But you see, as I say, the world doesn’t care about mathematics, it’s doing what it does, mathematics is just a tool.

Aarit: Yes I see what you mean. Another thing I was wondering is that, obviously your father was a noticeable scientist himself, so I was wondering how much has this impacted your journey and indeed your actions in science and academia?

Kosterlitz: My father was what is called a physiologist although he ultimately turned himself into what is called a neuropharmacologist. My parents never encouraged me or discouraged me from studying anything. So I was allowed to do what suited me and it turned out that mathematics and science, especially physics, happened to suit my way of operating. I seemed to be quite good at it and I liked the fact that one doesn’t have to remember too much and one could work things out without too much memory. I remember thinking that my classmates seemed to be able to remember a hell of a lot of facts, but these facts don’t really help you when you’re trying to solve a problem. So my parents didn’t influence what I studied, they let me do what I wanted to do. So I was lucky, I had a good education that suited me and I was able to follow my heart in this. I wasn’t forced to do finance or whatever to make money. I grew up in the 60s when I was a flower child and whatever nonsense. So I was allowed to do what I liked and not worry about the consequences. Basically, I decided that my main purpose in life is to have fun, because if you’re not having fun with what you’re doing, it’s not worth it. If you don’t enjoy what you’re doing, why do it? So I just happened to enjoy doing physics and mathematics, so I had a lot of fun doing it. I remember at school whenever we were introduced to a new piece of mathematics, I thought “wow”, I can suddenly solve problems I couldn’t do before.

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