  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.
