Stephen Hawking (1942-2018).

'The Occurrence of Singularities in Cosmology. II' Offprint from: Proceedings of the Royal Society, A, 295, pp.490-493. Cambridge: University Press, 1966.

Extraordinarily rare author's presentation copy – inscribed in Hawking's own hand – of one of his most important papers. After studying as an undergraduate at Oxford, Hawking moved to Trinity Hall, Cambridge for his graduate studies in October 1962. However, his first year at Trinity Hall coincided with the diagnosis of his motor neurone disease, leading to a period of depression in which he abandoned his studies, only resuming them after it became clear the prognosis that he had only two years to live was unfounded. The present work is one of a small number of Hawking's works that were personally inscribed by the author, before his worsening illness made this an impossibility.

In October 1965, Hawking submitted his PhD thesis, Properties of expanding universes, in which he examined the implications and consequences of the expansion of the universe. The final chapter looked at the occurrence of singularities [black holes] in cosmological models: 'It is shown that a singularity is inevitable provided that certain very general conditions are satisfied'. This set the direction of his future work – particularly in his interest in singularity theorems – as well as his style, combining popularising flair with a willingness to challenge received wisdom.

Consequently, in 1966, Hawking was awarded a research fellowship at Gonville and Caius, and he published two further papers on the occurrence of singularities (the present lot is the second one). This work would culminate in his extended essay Singularities and the geometry of space-time (December 1966), Hawking's prize-winning submission for the Adams Prize. In his introduction to this latter work, Hawking wrote: 'Undoubtedly, the most important results are the theorems in Chapter 5 on the occurrence of singularities. These seem to imply either that the General Theory of Relativity breaks down or that there could be particles whose histories did not exist before (or after) a certain time. The author's own opinion is that the theory probably does break down but only when quantum gravitational effects become important'.

The Adams Prize is awarded by the University of Cambridge for distinguished research in the mathematical sciences: it is one of the most prestigious of the university's prizes. Hawking's essay was joint-winner of the 1966 prize, alongside an essay by Roger Penrose, presaging an important period of close collaboration between the two over subsequent years.

Octavo (254 x 170mm), bifolium (heavy dampstain at bottom margin extending into last 5 lines of text, some light crumpling and creasing). Provenance: author's presentation copy inscribed 'With love, Stephen' in his hand to upper margin of first page – the estate of the late Professor Stephen Hawking.

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