The mass media announced on November 3, 2010 that
Yaroslav Sergeyev, a professor of Calabria University and Lobachevsky State
University of Nizhny
Novgorod, has received the Pythagoras Award. It was mentioned that “the
professor constructed and patented a new `Infinity Compute'” and
“he suggested
a new mathematical language that enables one to record various infinitely large
and infinitely small numbers.” This information requires commenting.
Sergeyev’s idea is to introduce into arithmetic some infinitely large
number—
grossone, consider only the numbers that are less than the grossone, and operate
exclusively on these numbers using the grossone as the radix.
Sergeyev embellishes his idea with metaphysical arguments,
emphasizing that he does not use Cantor’s approach and returns to
Ancient Greeks.
Elliot Mendelson remarked in his review of Sergeyev’s book [
1]
that “the systems he deals with consist of
objects which are called extended real numbers, but the descriptions of these
objects and their properties are not clear enough to permit any warranted
judgments about the assertions made by the author about these systems.”
Sergeyev confronts his ideas with the nonstandard analysis of Abraham
Robinson, defining his grossone as “the number of elements of the set of natural
numbers.” In fact, the role of this wouldbe mysterious entity can happily be
performed by the factorial of an
arbitrary infinite number which are galore in
nonstandard analysis. The principal shortcomings of Sergeyev’s
approach and attempts at implementing calculations with a grossone on a computer
were given in [
2].
Unfortunately, the series of Sergeyev’s
publications continues in the various international journals having little if any
in common with foundations of analysis. Miraculously, there are no Sergeyev’s
publications on his grossone in Russian.
Ancient Italian grossones are linguistically close to Sergeyev’s grossone but
differ in value.
References
 [1]

Sergeyev Ya. D., Arithmetic of Infinity. Edizioni Orizzonti Meridionali,
Cosenza (2003).
 [2]

Gutman A. E. and Kutateladze S. S.
"On the theory of grossone." Siberian Math. J.,
49:5, 835841 (2008).
Sobolev Institute of Mathematics
4 Koptyug Avenue
Novosibirsk, 630090
RUSSIA
November 7, 2010