Arend Heyting


Pioneer	Journal where reappraisal appeared	Title	Link to article containing reappraisal
Heyting	Intellectica	"Meaning in classical mathematics: Is it at odds with constructivism?"	11a

Heyting, Arend (1898-1980) was a mathematical Intuitionist whose lasting contribution was the formalisation of the Intuitionstic logic underpinning the semi-mystical Intuitionism of his teacher Brouwer. While Heyting never worked on any theory of infinitesimals, he had several opportunities to present an expert opinion on Abraham Robinson's theory. Thus, in 1961, Robinson made public his new idea of non-standard models for analysis, and "communicated this almost immediately to ... Heyting" (see Dauben 2003, 259). Robinson's first paper on the subject was subsequently published in Proceedings of the Netherlands Royal Academy of Sciences (Robinson 1961). Heyting praised non-standard analysis as "a standard model of important mathematical research" (Heyting 1973, 136). Addressing Robinson, he declared:

you connected this extremely abstract part of model theory with a theory apparently so far apart as the elementary calculus. In doing so you threw new light on the history of the calculus by giving a clear sense to Leibniz's notion of infinitesimals (ibid).

Intuitionist Heyting's admiration for the application of Robinson's infinitesimals to calculus pedagogy is in stark contrast with the views of constructivist Errett Bishop.