Stephen Hawking (1942-2018).

Photostatic copy typescript with autograph corrections and insertions, 'Singularities and the geometry of space-time', an essay submitted for the Adams Prize, Gonville and Caius College, Cambridge, 13 December 1966.

192 pages, 263 x 205mm, photostatic copy with the exception of one top-copy typescript slip of six lines pasted onto p.156; the autograph corrections and insertions comprise one equation added on p.19, one word inserted on p.87 ('curve'), three corrections on p.125 (substituting the word 'future' for 'past'), two insertions on p.137 in autograph ('and L are', 'and L'); one equation on p.136 and two partial equations on p.137 are perhaps in autograph; frequent manuscript corrections and overwriting in another hand throughout. Black cloth binding. Provenance: the estate of the late Professor Stephen Hawking.

Hawking's prize-winning submission for the Adams Prize. 'The aim of this essay is to investigate certain aspects of the geometry of the space-time manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions ... 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 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. Hawking had been awarded a research fellowship at Gonville and Caius earlier in 1966, after the grant of his PhD.

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