In Veltman's *Diagrammatica*, the full Lagrangian of the standard model is spelt out. This has around a hundred terms. This is way too many for even the most dedicated physicist (or physically inclined mathematician) to work on, except by piece by piece.

In the Connes-Lott-Barrett-Chamseddine model, based on non-commutative geometry, the standard model is derived from a spectral action with a simple geometric input, spacetime is multiplied with a 'fat' non-commutative point:

>$\mathbb{C} \oplus \mathbb{H}_L \oplus \mathbb{H}_R \oplus M_3(\mathbb{C})$


It is zero-dimensional, classically but has KO-theory dimension 6. This reproduces the full standard model including the Higgs and neutrino mixing. It turns out that the bimodule over the dual of this fat point, which is the sum of all irreducible irreps of odd dimension gives one full generation of the fermions. It's worth noting that the spectral action is a generalisation of the Einstein-Hilbert action. 

The theory is not limited to just the standard model. In a later paper with Chamseddine, Connes shows how NCG can model a grand unification theory like the Pati-Salam SU(5) GUT. 

Although non-commutative geometry is a geometry without a geometry. I mean by this that they work with a non-commutative algebra to be thought of as the algebra of functions on a non-commutative geometry which has not  bern constructed yet.  I'm not so sure that this will be the case in the near future (or perhaps the far near future given the density of maths required to understand and work with NCG). One of the standard examples of a non-commutative space, according to Connes,  is the irrational torus where classical tools do not give any information but non-commutative tools can. However, diffeology, which is a generalisation of classical differential geometry, does and it gives roughly similar results to that of Connes.