What do you see as the relationship between math and physics?

I prefer not to give you a cosmic answer but to comment on where we are now. Physics in quantum field theory and string theory somehow has a lot of mathematical secrets in it, which we don’t know how to extract in a systematic way. Physicists are able to come up with things that surprise the mathematicians. Because it’s hard to describe mathematically in the known formulation, the things you learn about quantum field theory you have to learn from physics.

I find it hard to believe there’s a new formulation that’s universal. I think it’s too much to hope for. I could point to theories where the standard approach really seems inadequate, so at least for those classes of quantum field theories, you could hope for a new formulation. But I really can’t imagine what it would be.

You can’t imagine it at all?

No, I can’t. Traditionally it was thought that interacting quantum field theory couldn’t exist above four dimensions, and there was the interesting fact that that’s the dimension we live in. But one of the offshoots of the string dualities of the 1990s was that it was discovered that quantum field theories actually exist in five and six dimensions. And it’s amazing how much is known about their properties.

I’ve heard about the mysterious (2,0) theory, a quantum field theory describing particles in six dimensions, which is dual to M-theory describing strings and gravity in seven-dimensional AdS space. Does this (2,0) theory play an important role in the web of dualities?

Yes, that’s the pinnacle. In terms of conventional quantum field theory without gravity, there is nothing quite like it above six dimensions. From the (2,0) theory’s existence and main properties, you can deduce an incredible amount about what happens in lower dimensions. An awful lot of important dualities in four and fewer dimensions follow from this six-dimensional theory and its properties. However, whereas what we know about quantum field theory is normally from quantizing a classical field theory, there’s no reasonable classical starting point of the (2,0) theory. The (2,0) theory has properties [such as combinations of symmetries] that sound impossible when you first hear about them. So you can ask why dualities exist, but you can also ask why is there a 6-D theory with such and such properties? This seems to me a more fundamental restatement.

Dualities sometimes make it hard to maintain a sense of what’s real in the world, given that there are radically different ways you can describe a single system. How would you describe what’s real or fundamental?

What aspect of what’s real are you interested in? What does it mean that we exist? Or how do we fit into our mathematical descriptions?

The latter.

Well, one thing I’ll tell you is that in general, when you have dualities, things that are easy to see in one description can be hard to see in the other description. So you and I, for example, are fairly simple to describe in the usual approach to physics as developed by Newton and his successors. But if there’s a radically different dual description of the real world, maybe some things physicists worry about would be clearer, but the dual description might be one in which everyday life would be hard to describe.

What would you say about the prospect of an even more optimistic idea that there could be one single quantum gravity description that really does help you in every case in the real world?

Well, unfortunately, even if it’s correct I can’t guarantee it would help. Part of what makes it difficult to help is that the description we have now, even though it’s not complete, does explain an awful lot. And so it’s a little hard to say, even if you had a truly better description or a more complete description, whether it would help in practice.

Are you speaking of M-theory?

M-theory is the candidate for the better description.

You proposed M-theory 22 years ago. What are its prospects today?

Personally, I thought it was extremely clear it existed 22 years ago, but the level of confidence has got to be much higher today because AdS/CFT has given us precise definitions, at least in AdS space-time geometries. I think our understanding of what it is, though, is still very hazy. AdS/CFT and whatever’s come from it is the main new perspective compared to 22 years ago, but I think it’s perfectly possible that AdS/CFT is only one side of a multifaceted story. There might be other equally important facets.