The Mathematical Intelligencer Flunks the Olympics

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence . We examine Sergeyev’s claims concerning his purported Infinity computer . We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework...

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Bibliographic Details
Published in:Foundations of science 2017-09, Vol.22 (3), p.539-555
Main Authors: Gutman, Alexander E., Katz, Mikhail G., Kudryk, Taras S., Kutateladze, Semen S.
Format: Article
Language:English
Subjects:
Beliefs, opinions and attitudes
Education
Infinity
Intelligence
Mathematical analysis
Mathematical Logic and Foundations
Mathematicians
Methodology of the Social Sciences
Philosophy
Philosophy of Science
Subsystems
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Summary:The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence . We examine Sergeyev’s claims concerning his purported Infinity computer . We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone , places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.
ISSN:1233-1821
1572-8471
DOI:10.1007/s10699-016-9485-8