Top-Down Design with Hyperlinks for Long Mathematical Proofs

Beyond mathematical complexity, a proof's length may, in and of itself, impede its comprehension. The same would apply to constructions, calculations and other mathematical expositions. Today's technology provides readers websites and electronic documents with hyperlinks, giving readers direct access from one location of the exposition to a different location. Using hyperlinks, electronic proofs may be presented in a top-down, modular format, making it possible for the reader to personalize the proof to the desired level of detail. To illustrate, a top-down proof of the Banach-Tarski theorem is given with live hyperlinks, permitting the reader to navigate the proof as they choose, with the precise level of detail required.