The
*Interfax Agency* and
other mass media announced on November 3, 2010
that
Yaroslav Sergeyev, a professor at
Lobachevsky State University of Nizhny Novgorod,
has received the
Pythagoras Award.
It was mentioned that
“the professor constructed and
patented
a new ‘Infinity Computer’”
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.
Sergeyev embellishes his idea with shallow arguments, emphasizing that he
does not use Cantor’s approach and returns to Ancient Greeks. He formulates
the three postulates of his own:

The scientific depth of Sergeyev’s postulates transpires.

Elliot Mendelson, an outstanding American logician whose textbook
was reprinted many times and is very popular in teaching throughout the world,
published the following
review on Sergeyev’s book *Arithmetic of Infinity*
which was printed in Italy in 2003:

The author attempts to introduce new kinds of number systems that he claims have
important applications. First, he reviews some facts about the ordinary number systems
and set theory. (Here, there is some confusion about alephs and the continuum
hypothesis. For example, he defines aleph-one to be the size of the power set of the
set of natural numbers.) 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 famous nonstandard analysis of Abraham Robinson. Robinsonian infinitesimal analysis is rightfully considered as one of the most brilliant achievements of mathematics in the twentieth century. Using the sophisticated methods of the recently-invented model theory in the beginning of the 1960s, Robinson synthesized the approaches by Newton and Leibniz in a new mathematical language and technique. Nonstandard analysis not only inherited all technical tools of Newton’s method of prime and ultimate ratios and Leibniz’s monads but also explained and justified the ingenious tricks of Euler who freely dealt with actual infinites and infinitesimals.

Sergeyev has poor knowledge of these classical scientific achievements, counterposing his bizarre surmisals to the modern analysis. But all linguistic and mathematical tools that are needed to Sergeyev are readily available within nonstandard analysis.

Sergeyev defines his *grossone*
as the “number of elements of the set of natural numbers.”
In fact, the role of this would-be mysterious entity
can happily be performed by the factorial of
an **arbitrary** infinite number which are galore in nonstandard analysis.
This circumstance is absolutely evident to specialists but
nonetheless it was meticulously elaborated in
*Siberian Mathematical Journal, 49:5, 835–841 (2008)*
in order to demonstrate the humble place of Sergeyev’s speculations.
This article also revealed the principal shortcomings
of Sergeyev’s attempts at implementing calculations with a grossone
on a computer.
Unfortunately, it turned out impossible to stop the
flood of
Sergeyev’s publications in the variety of the international journals
having little if any in common with foundations of analysis.
Miraculously, there are no Sergeyev’s publications on his grossone
in Russian in the Russian mathematical database
Math-Net.Ru.

Sergeyev’s writings about invention of new numbers and the “Infinity Computer” are speculations of negligible interest to mathematics but exuberant with pretensions, which might be perilous to science. The fact that these speculations underlie the Pytharogas Award by the City of Crotone on behalf of the University of Calabria having Sergeyev on staff cannot improve neither the content of the writings of Sergeyev nor his attitude to the precious knowledge of the treasure-trove of mathematics.

Ancient Italian grossones are linguistically close to Sergeyev’s grossone but differ in value.

S. Kutateladze

November 5, 2010

Preprint No. 250, Novosibirsk: Sobolev Institute of Mathematics (2010).

Letter to Professor Evgeny Chuprunov, Rector of Lobachevsky Nizhny Novgorod University.

Excerpt from the description of the

La finalità è quella di attrarre nuovi segmenti di turisti nella città e di favorire lo sviluppo di nuove attività economiche nel settore dei servizi per la fruizione e valorizzazione del patrimonio culturale.

Manlio Gaudioso, Professore ordinario presso l'Universita della Calabria,

Federico Pedrocchi, giornalista scientifico, redattore e presentatore della trasmissione Moebius di Radio Sole 24 Ore.

Newsletter of the European Mathematical Society, No. 79, March, 2011, p. 60;

J. Appl. Indust. Math., 2011, V. 5, No. 1, 73–75.

English Page |
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© Kutateladze S. S. 2011