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December 2005 Over the millennia, many mathematicians have hoped that mathematics would one day produce a Theory of Everything (TOE); a finite set of axioms and rules from which every mathematical truth could be derived. But in 1931 this hope received a serious blow: Kurt Gödel published his famous Incompleteness Theorem, which states that in every mathematical theory, no matter how extensive, there will always be statements which can't be proven to be true or false. Gregory Chaitin has been fascinated by this theorem ever since he was a child, and now, in time for the centenary of Gödel's birth in 2006, he has published his own book, called Meta Math! on the subject (you can read a review in this issue of Plus). It describes his journey, which, from the work of Gödel via that of Leibniz and Turing, led him to the number Omega, which is so complex that no mathematical theory can ever describe it. In this article he explains what Omega is all about, why maths can have no Theory of Everything, and what this means for mathematicians."

"One of the best aspects of science has always been its readiness to admit when it got something wrong. Theories are constantly being refigured, and new research frequently renders old ideas outdated or incomplete. But this hasn't stopped some discoveries from being hailed as important, game-changing accomplishments a bit prematurely. Even in a field as rigorous and detail-oriented as science, theories get busted, mistakes are made, and hoaxes are perpetrated. The following are ten of the most groundbreaking of these scientific discoveries that turned out to be resting on some questionable data. It is worth noting that most of these concepts are not necessarily "wrong" in the traditional sense; rather, they have been replaced by other theories that are more complete and reliable."