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.

See also

Fermat

Euler

Cauchy

Cantor

Skolem

Bishop

Robinson

Nelson

Hrbacek

Kanovei

Infinitesimal topics

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