English
mathematician who formulated some of the fundamental theorems that describe
black holes, including the singularity theorems, developed jointly with
English physicist Stephen Hawking, which state that once the gravitational
collapse of a star has proceeded to a certain degree, singularities
(which form the centre of black holes) are inevitable. Penrose has also
proposed a new model of the universe.

Penrose was born in Colchester, Essex, and studied at University College,
London. While he worked for his doctorate at Cambridge in 1957, Penrose
and his father were devising geometrical figures, the construction of
which is three-dimensionally impossible. (They became well known when
incorporated by Dutch artist M C Escher into a couple of his disturbing
lithographs.) Penrose was professor at Birkbeck College, London, 1966-73,
and then moved to Oxford University.

The existence of a trapped surface within an 'event horizon' (the interface
between a black hole and space-time), from which little or no radiation
or information can escape, implies that some events remain hidden to
observers outside the black hole. Penrose has put forward the hypothesis
of 'cosmic censorship' - that all singularities are so hidden - which
is now widely accepted.

Calculations in the world of ordinary objects (including Einstein's
general theory of relativity) use real numbers, whereas the world of
quantum theory often requires a system using complex numbers, containing
imaginary components that are multiples of the square root of 1. Penrose
holds that all calculations about both the macroscopic and microscopic
worlds should use complex numbers, requiring reformulation of the major
laws of physics and of space-time. He has proposed a model of the universe
whose basic building blocks are what he calls 'twistors'.

His works include The Emperor's New Mind: Concerning Computers, Minds,
and the Laws of Physics 1989 and Shadows of the Mind: A Search for the
Missing Science of Consciousness 1994.