On Gödel's and Nagel's contrasting views on the possible significance of Gödel’s theorems for minds vs. machines in the development of mathematics.

Call a program "elegant" if no smaller program has the same output. I.e., a LISP S-expression is defined to be elegant if no smaller S-expression has the same value. It is impossible to prove that any particular large program is elegant.

A crash course in the mathematics behind Turing's results and how it applies to the very practical problem of programming in C. Explains the connection between Turing Machines, Lambda Calculus, types, Classical Logic and proofs.

It begins to look like randomness is a unifying principle. We not only see it in quantum mechanics and classical physics, but even in pure mathematics, in elementary number theory.

Conjecture: Uncertainty implies algorithmic randomness not only in mathematics, but also in physics.

Chaitin compares and contrasts Gödel's, Turing's and his own work in a straight-forward manner using Lisp.

Gödel's Incompleteness Theorem is not an obstacle to Artificial Intelligence.

If a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. This suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread [..].

Answers to some of the frequently asked questions received since the publication of the Gödel Machine TR in 2003.

Gödel machines are self-referential universal problem solvers making provably optimal self- improvements.

J. Andrew Rogers' argument against add-on Friendliness (the self-modeling Gödel problem).