Irreducible complexity in pure math

Invited Talk by Gregory J. Chaitin, IBM Research at MKM 2006

We'll discuss the halting probability Omega, whose bits are irreducible mathematical facts, that is, facts which cannot be derived from any principles simpler than they are. In other words, you need a mathematical theory with N bits of axioms in order to be able to determine N bits of Omega. This pathological property of Omega is difficult to reconcile with traditional philosophies of mathematics, with traditional views of the nature of mathematical proof and of mathematical knowledge. Instead Omega suggests a quasi-empirical view of math that emphasizes the similarities between mathematics and physics rather than the differences.

Maintained by: Dr Andrew A. Adams (Conference Chair)
Last modified: Sun Mar 5 12:42:41 GMT 2006