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