Foundations of Science

, Volume 22, Issue 3, pp 539–555 | Cite as

The Mathematical Intelligencer Flunks the Olympics

  • Alexander E. Gutman
  • Mikhail G. Katz
  • Taras S. Kudryk
  • Semen S. Kutateladze
Article

Abstract

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.

Keywords

Mathematical Intelligencer Nonstandard Analysis Transfer Principle Conservative Extension Algorithmic Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We are grateful to Rob Ely for helpful suggestions. We thank the anonymous referee for Foundations of Science for helpful comments. M. Katz was partially funded by the Israel Science Foundation Grant No. 1517/12.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Alexander E. Gutman
    • 1
  • Mikhail G. Katz
    • 2
  • Taras S. Kudryk
    • 3
  • Semen S. Kutateladze
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia
  2. 2.Department of MathematicsBar Ilan UniversityRamat GanIsrael
  3. 3.Department of MathematicsLviv National UniversityLvivUkraine

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