The Robbins problem: computer proofs and human proofs

Abstract

Discusses the relationship between computer proof and human proof. These issues are discussed both in general and specifically regarding the recent solution of the Robbins problem via a proof generated by computer. The Robbins problem was a long-standing open problem about axioms for Boolean algebra. One point of this paper is to show that the proof of the Robbins conjecture, generated by a computer, can be filled in and understood by human beings. We accomplish this aim in the present paper by presenting a notational reformulation of Boolean algebra and the Robbins problem. The notational/linguistic issue developed here is of cybernetic, linguistic and semiotic interest. It is our contention that mathematics can behave non-trivially under change of notation. Change of notation can be as significant as change of language. In the present case the change of language afforded by an appropriate change of notation makes a mathematical domain accessible to human beings that has heretofore been only accessible to computers. Kybernetes, Vol. 30 No. 5/6, 2001, pp. 726-751. # MCB University Press, 0368-492X