An attempt is made to apply information-theoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms. 2 G. J. Chaitin Key Words and Phrases: complexity of sets, computational complexity, difficulty of theoremproving, entropy of sets, formal systems, Godel's incompleteness theorem, halting problem, information content of sets, information content of axioms, information theory, information time trade-offs, metamathematics, random strings, recursive functions, recursively enumerable sets, size of proofs, universal computers CR Categories: 5.21, 5.25, 5.27, 5.6 1. Introduct...