Fixed-Point Theorems in Analysis, Logic, and Computer Science
A brief survey of some fixed-point theorems in mathematics, including:
Banach's fixed-point theorem (the contraction mapping theorem)
Gödel / Carnap's fixed-point lemma (the diagonal lemma), with an application to Gödel's first incompleteness theorem for Peano arithmetic
Fixed-point combinators of Curry (Y combinator) and Turing (Theta combinator) in the lambda calculus