4th Refinement Workshop pp 115-124 | Cite as

# Formal Methods and the Sociology of Proof

## Abstract

This paper begins by asking whether a sociology of mathematical knowledge is possible. Having answered in the affirmative (drawing examples from the history of mathematics), it goes on to discuss the development of a similar analysis of the mathematical aspects of computer science. A brief vignette is presented: the processes of negotiation of the IEEE floating-point arithmetic specifications. Then the discussion moves on to the verification of software and hardware. If the sociology of mathematics is correct, then formal proofs can be seen as social, not just in the processes of their acceptance, as de Millo, Lipton and Perlis [DLP79) have argued, but also in their internal structure. Placed in the context of pressure for formal verification of safety-critical and security-critical systems, this argument led the author and colleagues to the prediction, three years ago, that litigation involving the nature of mathematical proof was bound to occur. That prediction has now been borne out.

## Keywords

Formal Method Formal Proof Mathematical Proof Computer Arithmetic Informal Proof## Preview

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