The next chapter is likely to provoke many mathematicians. This can't be helped. Mathematics is not what they… — David Deutsch

The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation—the only one that is tenable—of a remarkable and counter-intuitive reality.

Reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical.

Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.