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Nature 444, 1018-1019 (21 December 2006) | doi:10.1038/4441018a; Published online 21 December 2006
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Professor of Psychosomatic Medicine (W2)
- The University Hospital Jena, Institute of Psychosocial Medicine and Psychotherapy
- Jena Germany
Molecular Biologists and Biochemists
- University of Minnesota
- Minnesota, USA
Mathematics: Proof at a roll of the dice
Bernard Chazelle1
Abstract
The PCP theorem encapsulates the idea that randomization allows the immediate verification of any mathematical proof. A simple route to this striking result was proposed earlier this year.
Many branches of mathematics have their signature numbers: geometry has the transcendental 
; analysis Euler's exponential e; and algebra the imaginary unit, the square-root of -1, i. These numbers are the stars of exotic — but seemingly quite separate — worlds scattered across the vast expanse of the mathematical cosmos.
- Bernard Chazelle is in the Department of Computer Science, Princeton University, 35 Olden Street, Princeton, New Jersey 08540-5233, USA.
Email: chazelle@cs.princeton.edu
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