The Mathematical Intelligencer flunks the Olympics

TL;DR

The paper critically examines Sergeyev's Infinity computer and grossone system, comparing it with classical mathematical frameworks, and concludes that grossone is unnecessary, vague, and subsumed by more robust systems.

Contribution

It provides a detailed comparison of Sergeyev's grossone system with classical theories, demonstrating its redundancy and lack of clarity.

Findings

Grossone system is unnecessary and vague.

Classical frameworks like Levi-Civita fields and hyperreals are more robust.

Grossone is outside the historical context of infinity and infinitesimals.

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.