Person: Heyting, Arend
Arend Heyting is important in the development of intuitionistic logic and algebra.
Mathematical Profile (Excerpt):
- Both Arend's parents were school teachers and Johannes Heyting was particularly successful in his profession being appointed as head of a secondary school.
- Arend spent his school years with the intention that he would make a career in engineering.
- At the University of Amsterdam Heyting was taught by Brouwer who had a large influence on his future work.
- In 1922 Heyting graduated with a degree of master's standard.
- At this point in his career Heyting began to follow the same road as his parents by beginning a career as a secondary school teacher.
- Heyting was not well placed to make contact with colleagues in the universities, yet he spent all his free time working on his research.
- When the Dutch Mathematical Association announced a prize question in 1927 they gave Heyting an ideal topic on which to compete.
- They asked for a formalisation of Brouwer's intuitionist theories and Heyting's outstanding essay was awarded the prize in 1928.
- This essay was then polished and expanded by Heyting and published in 1930.
- It made Heyting's name well known among those interested in the philosophy of mathematics.
- This work had another beneficial effect as far as Heyting was concerned for it brought him to the attention of Heinrich Scholz who held the chair of mathematical logic in Münster.
- Scholz made his extensive library available to Heyting, fortunate since Münster was relatively close to Enschede, and a lifelong friendship arose between the two.
- Heyting's academic isolation in Enschede no longer seemed the problem that it might have been.
- Heyting attended the Erkenntnis Symposium at Königsberg in September 1930.
- Although Heyting's version of intuitionist logic differed somewhat from that of Brouwer, it is clear that one of his main aims was to make Brouwer's ideas more accessible and better known.
- There were others interested in intuitionist logic working on similar problems of formalisation at the same time as Heyting.
- One was Kolmogorov who corresponded with Heyting.
- Heyting was appointed as a Privatdozent at the University of Amsterdam in 1936 and in the following year he was appointed as a lecturer.
- Heyting published a paper on intuitionistic algebra in 1941 and intuitionistic Hilbert spaces in the 1950's.
- Franchella argues that Heyting has been the cause of two major changes of direction.
- Heyting moved away from these big problems, concentrating on trying to identify formal, intuitive, and logical concepts in the study of mathematics.
- The second change which Franchella argues that Heyting brought about was a realisation that there exist degrees of evidence in mathematics.
- We should end this biography by giving an indication of Heyting's personality.
Born 9 May 1898, Amsterdam, Netherlands. Died 9 July 1980, Lugano, Switzerland.
View full biography at MacTutor
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive