We show that the mathematical proof of the four colour theorem directly implies the existence of the standard model together with quantum gravity in its physical interpretation. Conversely, the experimentally observable standard model and quantum gravity show that nature applies the mathematical proof of the four colour theorem at the most fundamental level. We preserve all the established working theories of physics: Quantum Mechanics, Special and General Relativity, Quantum Electrodynamics (QED), the Electroweak model and Quantum Chromodynamics (QCD). We build upon these theories, unifying all of them with Einstein's law of gravity. Quantum gravity is a direct and unavoidable consequence of the theory. The main construction of the Steiner system in the proof of the four colour theorem already defines the gravitational fields of all the particles of the standard model. Our first goal is to construct all the particles constituting the classic standard model, in exact agreement with 't Hooft's table. We are able to predict the exact mass of the Higgs particle and the CP violation and mixing angle of weak interactions. Our second goal is to construct the gauge groups and explicitly calculate the gauge coupling constants of the force fields. We show how the gauge groups are embedded in a sequence along the cosmological timeline in the grand unification. Finally, we calculate the mass ratios of the particles of the standard model. Thus, the mathematical proof of the four colour theorem shows that the grand unification of the standard model with quantum gravity is complete, and rules out the possibility of finding any other kinds of particles. We show how to calculate Einstein's cosmological constant using the grand unified theory. Using the topological properties of the gauge, we calculate the exact percentages of ordinary baryonic matter, dark matter and dark energy in the universe. These values are in perfect agreement with the seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations. Thus dark matter, dark energy and the cosmological constant are intrinsic properties of the gauge in the grand unified theory.