Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"The impossible puzzle," by Michael Brooks.New Scientist, 5 April 2003,pages 34-35.

This article reports on a lecture presented by the renowned physicist StephenHawking at the Diraccentennial celebration at the University of Cambridge. In the lecture,entitled "Gödel and the end of physics," Hawking presented the startlingidea that there may be a fundamental obstruction to a "theory of everything."The work of the mathematician Kurt Gödel showed that any mathematicalsystem contains self-referential statements that are not provable within thatsystem. Models of the physical universe might have this same kind ofincompleteness, Hawking suggested. "We and our models are both part of theUniverse we are describing," Hawking is quoted as having said. "We are notangels who view the Universe from outside." As Brooks explains, this meansthat physical theories can be self-referential, so "we shouldn't be surprisedif they are inconsistent or incomplete."

--- Allyn Jackson