What is all the matter in the universe made of? We know that most matter is made of atoms - and the bulk of the mass in an atom is concentrated in the nucleus. Nuclei can be described as made of protons and neutrons. The proton and neutron are known to be extended objects - so not "elementary".

In the 1970s, a theory was proposed to explain what the proton and neutron are made of. This is Quantum Chromo Dynamics (QCD). This is a very remarkable theory - the basic ingredients are quarks and gluons but these ingedients can only exist as composites - such as the proton and neutron. The gluons are massless and the relevant quarks (up(u) and down(d)) have a mass only a small percentage of that of a proton or neutron. So where does the proton's mass come from? The theory is that the gluons stick quarks together, but also stick to each other - which produces the required mass.

People, citing the Higgs particle, claim it is responsible for mass - this is partly true, it is thought to be responsible for the mass of the quarks, but very misleading: the bulk of the mass of every atom comes from the gluonic force in QCD.

A simplified situation in which this mass generation can be studied, is the world containing only gluons (also described by QCD). The gluons are massless, but the lightest state, named the glueball, turns out to have a significant mass - similar to that found in the proton and neutron.

Proving this, mathematically, is one of the million dollar Clay prize challenges. My work, with partners, has mapped out the masses and properties of the glueballs. The method used is computational, so falls short of the "proof" Clay require to pay up.

So how do you get a computer to tackle QCD?. A quantum field theory can be represented as a sum over all possible fields, with a specified and calculable weighting factor. This is a challenge: we have 4 space-time coordinates and (for gluons) an internal 8-dimensional space [a bit like the surface of a sphere, but more complex]. So the gluon field has 8 internal dimensions, lives in 4 extensive dimensions, and we have to sum over all possible such fields. The solution is to simplify: use a finite grid of space time [known as the lattice]; and select representative gluon fields [rather than sum over all]. This was a problem that occurred in designing the atom bomb - and Monte Carlo simulation, with clever algoriths [Metropolis] were devised to pick representative contributions.

However, one more big cheat is required. The weighting factor in QCD can be both positive and negative. This mucks up the algorithm that would pick representative fields. The solution is to work in "imaginary time". This may sound absurd, but it amounts to exploring a world with 4 space dimensions. Fairly convincing arguments exist that the masses of the glueballs found in such a world are simply related to those in the real world.

So job done - get a super computer - work on small lattices at first, then extrapolate to large lattices with smaller gaps between the points.

Further details are contained in my memoirs - but aimed at professionals in the field.