This is an expanded and illustrated version of an essay originally published in the Cambridge Review to mark Stephen Hawking’s 50th birthday. It explores such questions as how cosmology is possible at all and examines key theories from ancient times and the scientific revolution as well as modern developments.

It explains the relativistic concept of space-time and shows how Einstein interpreted gravitation as its curvature. Einstein’s theory forms the basis for all contemporary cosmological models of the expanding universe. But it is faced with the paradoxical implication that the Universe began with an Initial Singularity at which the theory itself breaks down since all physical quantities would become either ‘zero’ or ‘infinite’.

There have been various attempts to circumvent this paradoxical prediction about the Universe’s earlier moments, which appear in practice to be largely shrouded by the event whose dull echo we now observe in the Cosmic Microwave Background. Hartley and Hawking have proposed a so-called ‘No Boundary’ model to avert the idea of ‘creation’ by introducing ‘imaginary time’. Penrose on the other hand holds the observations are consistent with endless ‘Cycles of Time’ in which the ultimate featureless state of one universe loses all sense of scale and so become indistinguishable from the initial state of a subsequent universe.

This essay examines how the unfolding story has been driven by mathematical ideas but raises questions about the nature of mathematical truth itself. There is a widespread desire to integrate cosmological theory into an overarching narrative which gives significant to human life, but this should not influence what is ‘believed’ in the absence of actual evidence.

Our understanding of the world will remain incomplete so long as we are unable to integrate the fact of consciousness with the picture of the world which is embedded in physical theory. This raises the question whether the mathematical character of the physical world is something which is inherent in nature itself, or whether it is imposed on nature by us.

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