Baths would be so much more relaxing if they weren't so interesting. There are so many amazing things.  Bubble rings, there is something strange and unnatural about these objects, some structure where you wouldn't expect to see structure. When I get out of the bath and pull the plug, there is a whorl of water that drains away, a vortex. It is very similar to the bubble rings. And objects like these may just hold the key to one of the most important problems in physics. 
My name is David Tong, my job is to understand the beautiful things that I see in the world around me. But to describe these properly I have to understand them in the language in which nature is written, mathematics.
When I use equations to understand bath water, one of the nice things I can see is that the bubble rings and the whorl of water, the vortex that appears when you pull the plug, are just examples of the same object.
The bubble ring is a whorl of water that is joined together to form a circle. Us physicists have a name for these. We call them solitons. The name comes from the unique solitary nature of these objects.
It takes rather special conditions to get a soliton to form. For example I have to stick my hand in the tank and swirl it round so the whole water knows to move together as one. The way they form in air and water is that you exert some pressure on the liquid or the gas and pass it over an obstacle for example your tongue if you're blowing bubble rings so that the water and air has some swirls in it that give rise to the soliton. 
What are these strange objects called solitons?
Usually if you look at water or air, all the molecules are moving around at random. But in a soliton an entire body of water or air is moving coherently, swirling as one. And right in the centre in the eye of the storm, there is actually a complete absence of water, that is the soliton. What's happening is any molecule that was in there gets some kind of identity crisis. To one side of the tank water molecules are saying go that way, go that way. And to the other side they are saying go that way, go that way. And it doesn't know where to go and so it just gets out of the way. And what's left is this empty hole, that's the vortex. 
In a Zen like manoeuvre we view this absence of water as an object in its own right. 
There are many places in the natural world where solitons form. Smoke rings in air are an example of a soliton as are vast tornados in the atmosphere. They also appear in optical fibres and superconductors. There are even suggestions that there might be solitons stretched across the entire universe. 
Solitons are beautiful objects but as I look deeper into the world at smaller and smaller distances I see solitons everywhere. And right at the very heart of matter, solitons hold the answer to the most important question. What is holding everything together?
Strangely the best way to understand what holds everything together is to smash it to bits. You take it and you just hit it really really hard. So hard that it falls apart and reveals what is inside. 
It's how we understood what atoms are made of. There is a nucleus. The nucleus contains protons and neutrons but inside these protons and neutrons are three smaller particles. These are quarks and the strange thing about a quark is no one has ever seen one on its own. 
If you try to pull a quark out of a proton a soliton forms. It is like a vortex but it has this strange elastic property and it pulls the quark back into the proton. It doesn't matter how hard you pull. You can never pull hard enough to beat this elastic band, this vortex. And that's what holds everything together. 
There are sophisticated computer simulations that show this soliton forming around quarks. Remarkably it really does look like a couple of marbles and an elastic band. If quarks weren't trapped inside protons then everything would fall apart.
The whole universe depends on these solitons existing. 
[David Tong discusses formulas with students]
Other particles don't form solitons when you hit them. So why does it happen for quarks, why is it just quarks that get trapped? No one knows.
[Tong discusses QCD (Quantum ChromoDynamics) with a student]
It is a complete mystery. For 40 years scientists have been working on this and no one has figured out the answer yet. 
It was recently voted one of the seven most important problems in mathematics. There is a prize of a million dollars for anyone who can solve it. And yet it remains as mysterious as ever.
When I have got to solve a problem this hard, I take long long baths, I have long walks. Sit down and stare at a piece of paper for hours on end trying to even think about the equation that I put on top of the paper.
I try and scribble equation after equation just seeing if there is some thread of the equation that I can pull off, somewhere to start, somewhere to start unravelling the difficulties of this problem. 
I've got a football in my office that I kick around outside. Kicking the football helps me think. 
For the last 5 years I have been thinking about this. Trying to figure out why those quarks get stuck inside the protons. But it is such a hard problem. So instead I took a slight sidestep. I started thinking about other particles and how those particles would interact with each other. And there everything worked perfectly. I understood how the solitons would form and how they would move, how the solitons would trap those particles and stop them escaping. It was a beautiful, excellent solution. Unfortunately it was the solution to the wrong problem. 
I feel that there should be a simple solution to this problem, that there should be a solution as easy as describing the vortex in my bath water. But without it there is something really fundamental and important about our universe that we don't understand. And that really bugs the hell out of me. 
