Hawking, who was born in Oxford, graduated from the university there and obtained his PhD from Cambridge University. After holding various Cambridge posts, he became professor of gravitational physics in 1977 and, in 1979, was appointed Lucasian Professor of Mathematics.

Hawking worked mainly in the field of cosmology, in particular the theory of black holes. In 1965 Roger Penrose had shown that a star collapsing to form a black hole would ultimately form a singularity – a point at which the density of matter is infinite and at which there is an infinite curvature of space–time. Hawking realized that by reversing the time in Penrose's theory he could show that the big bang originating the Universe must also have come from a singularity. Similarly, if the Universe were to stop expanding and start contracting it would eventually end at a singularity – the so-called ‘big-crunch’. Penrose and Hawking published these results in 1970. The results of Hawking's work using general relativity were summarized in a book with George Ellis, The Large Scale Structure of Spacetime (1973).

In fact, at a singularity, with infinite curvature of space–time, the general theory of relativity breaks down and consequently it cannot be applied to the origin of the Universe. This led Hawking to the application of quantum theory to the gravitational interaction. Of the four fundamental interactions, the strong, weak, electromagnetic, and gravitational interactions, the gravitational interaction is the only one not described by quantum theory. The others occur at distances comparable to the sizes of atomic particles and quantum effects are important. Gravitational interactions between masses over long distances are important in cosmology and can be described by the nonquantum theory of relativity. However, at the vanishingly small distances necessarily occurring just after the big bang (or just before a total collapse), quantum effects would be important. Hawking and others turned their attention to quantum gravity.

So far, the general application of quantum mechanics to gravitational interactions has had limited success. One notable discovery has been Hawking's theory showing that black holes are not in fact ‘black’ – they effectively emit energy as if they were a hot body.

The basis of the mechanism behind ‘hot’ black holes is the Heisenberg uncertainty principle. According to this free space cannot be empty because a point in space would then have zero energy at a fixed time and this would contradict the principle. In space, pairs of virtual particles and antiparticles are constantly forming and annihilating. One member of the pair has a positive energy and the other has a negative energy. Under normal conditions a virtual particle does not exist in isolation and is not detected. However, Hawking showed that in the vicinity of a black hole it is possible for the particles to separate. The negative-energy particle can fall into a black hole and its partner may escape to infinity, appearing as emitted energy.

The theory resolves a problem concerning the thermodynamics of black holes. If matter of high entropy falls into a black hole then there has been a net entropy loss unless the black hole itself gains entropy. One interpretation of the entropy of a black hole is its area, which increases whenever matter falls into the hole. However, if a black hole has an entropy it must also have a temperature. Hawking showed that the emission of energy from a black hole was distributed as if it were radiated from a black body at the appropriate temperature.

A black hole produced by a collapsing star would have a temperature within a few millionths of a degree above absolute zero. Hawking speculated on the existence of ‘mini black holes’ weighing a billion tons but having a size no bigger than a proton (about 10^–15 meter). These could be produced during the early stages of the big bang and are consequently known as ‘primordial black holes’. Because of their small size they would radiate gigawatts of energy in the X-ray and gamma-ray regions of the electromagnetic spectrum. So far there is no experimental evidence for their existence.

Hawking innovatively applied quantum gravity to the question of the origin of the Universe, making various modifications to the inflationary theory first proposed by Alan Guth. He also put forward an original proposal for the origin and evolution of the Universe applying the ‘sum over histories’ formalism of quantum mechanics of Richard Feynmann. Hawking's model of the Universe is conceptually difficult. It involves an Euclidean space–time in which time is an imaginary quantity (in the mathematical sense). There are no singularities at which the laws of physics break down; space–time is finite but closed, having no boundaries, and no beginning or end.

Hawking is generally regarded as one of the foremost theoretical physicists of the last fifty years, and this despite a severe physical disability. In the early 1960s he developed motor neurone disease and from the end of that decade he was confined to a wheelchair. Most of his communication was through a computer speech synthesizer. Of this, Hawking said that he “was fortunate in that I chose theoretical physics, because that is all in the mind.” In 1988 Hawking published a popular account of cosmology, A Brief History of Time. The book and its author captured the public imagination and made Hawking an international celebrity, even to noncosmologists. In it he looked forward to a time when a complete theory could be found understandable to everyone. “If we find the answer to that, it would be the ultimate triumph of human reason – for then we would know the mind of God.”