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Sinkevich G. The Fate of Russian Translations of Cantor// Notices of the International Congress of Chinese Mathematicians. International Press of Boston. 2015. - V.3, No 2, p. 74-83.

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Abstract

This is the history of translating Cantor’s works into Russian from 1892 to 1985 in Odessa, Moscow, Tomsk, Kazan, S.-Petersburg, Leningrad. Mathematicians and philosophers in Russia took the ideas of the theory of sets enthusiastically. Such renowned scholars and scientists as Timchenko, Shatunovsky, Vasiliev, Florensky, Mlodzeevsky, Nekrasov, Zhegalkin, Yushkevich Sr., Fet, Yushkevich Jr., Kolmogorov, and Medvedev took part in their popularisation. In 1970 Academician Pontryagin rated the theory of sets as useless for young mathematicians, and the translated works of Cantor were not published. This article first describes the tragic fate of this translation.
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The Fate of Russian Translations of
Cantor
by Galina Sinkevich*
Abstract. This is the history of translating Cantor’s
works into Russian from 1892 to 1985 in Odessa,
Moscow, Tomsk, Kazan, S.-Petersburg, Leningrad.
Mathematicians and philosophers in Russia took the
ideas of the theory of sets enthusiastically. Such
renowned scholars and scientists as Timchenko,
Shatunovsky, Vasiliev, Florensky, Mlodzeevsky,
Nekrasov, Zhegalkin, Yushkevich Sr., Fet, Yush-
kevich Jr., Kolmogorov, and Medvedev took part in
their popularisation. In 1970 Academician Pontryagin
rated the theory of sets as useless for young
mathematicians, and the translated works of Cantor
were not published. This article first describes the
tragic fate of this translation.
MSC 2010 subject classifications: 01A60, 01A70,
01A85.
I
From 1872 to 1897, Cantor wrote his basic works
devoted to the theory of sets. Russian mathemati-
cians who visited universities of Berlin and Gottingen
and read Crelle’s Journal, Mathematische Annalen,
Acta Mathematica got to know the ideas of the theory
of sets. Cantor’s ideas gradually permeated research
activities and teaching, appeared in press in the form
of expositions and translations. We are going to re-
view the history of Cantor’s heritage in Russia from
1892 to 1985.
*St. Petersburg State University of Architecture and Civil En-
gineering, St. Petersburg, Russia
E-mail: galina.sinkevich@gmail.com
Odessa, 1892. I. Y. Timchenko
Ivan Y. Timchenko (1863–1939).
We found the first references (1892) to Can-
tor’s works in Russia in works of Ivan Y. Timchenko
(1863–1939) who graduated from Novorossiysk Uni-
versity in Odessa in 1885 to subsequently become a
professor in Odessa. Timchenko studied astronomy,
mathematics and history of mathematics, travelled
abroad to work in libraries (in 1890, 1892, 1893, and
1896). Timchenko chose historical analysis of devel-
opment of the theory of analytical functions as the
subject of his MPhil. His work entitled “Basis of the
theory of analytical functions” was published in three
editions of “Proceedings of the Department of Mathe-
matics of Novorossiysk Scientists” in 1892 and 1899,
and presented in 1899 [T1, T2].
His in-depth research covers the period from the
ancient world to the late 19th century. In this work,
he considered development of basic ideas underly-
ing the theory of analytical functions. The most im-
portant of these ideas is the concept of continu-
ity and related concepts of neighbourhood and limit
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point. Timchenko pays tribute to Weierstrass in the
development of the concept of neighbourhood and
uniform convergence of series, and to Georg Can-
tor in the geometrical treatment of the concept of
continuity in his works devoted to linear manifolds.
Timchenko points out the relationship between Can-
tor’s apprehension of continuity (“integrity” accord-
ing to Timchenko) and Leibniz’ principle of conti-
nuity [T1, p. 12]. Notably, Timchenko addressed the
key works of Cantor. The first one was his work
of 1872, “Ueber die Ausdehnung eines Satzes aus
der Theorie der trigonometrischen Reihen”, where a
new concept of a number and a concept of a lim-
iting point were introduced. Mathematicians like H.
Schwartz and U. Dini [DU] who used to give the
course of analysis happily picked up this idea. The
second and most famous one is the Fifth Memoir
(Ueber unendliche lineare Punktmannigfaltigkeiten)
from the cycle which comprises 6 parts published in
1879–1884. This work is entitled “Grundlagen einer
allgemeinen Mannigfaltigkeitslehre”. It contains all
basic definitions and theorems, including the defi-
nition of the empty set, perfect set, concept of the
real number and its benchmarking compared to sim-
ilar concepts of Weierstrass and Dedekind; it intro-
duces a power scale and sets the continuum hypoth-
esis.
Odessa, 1896. S. O. Shatunovsky
Samuil O. Shatunovsky (1859–1929).
Samuil Osipovich Shatunovsky (1859–1929) was
born to a poor family of a Jewish artisan. He did
not obtain a systematic education, having attended
various learning institutions in Russia and Switzer-
land. For a long time Shatunovsky earned his liv-
ing giving lessons in small provincial towns. He
used to write works in math devoted to issues
in geometry and algebra, axiomatic determination
of a value; published them in Russian and for-
eign journals, and kept track of European mathe-
matical life. Shatunovsky appeared in Odessa be-
tween 1891 and 1893. Owing to Odessa profes-
sors, Shatunovsky was as an exception allowed to
take examinations for Master’s degree which opened
for him the door to teaching [Ch]. Shatunovsky
was granted the position of privat-docent only
when he was almost 47, and after 1917 he be-
came a professor of Novorossiysk University. Since
1905, Shatunovsky was reading analysis using defi-
nitions and methods of the theory of sets. The first
concepts of mathematical analysis were set forth
from the perspective of the theory of sets. How-
ever, Russian terms differed from the contempo-
rary ones. Thus, a set, for example, was called a
“complex”. He constructed a real numbers system
and, introduced the concept of a convergent com-
plex (dense set). He was the first to introduce the
concept of a removable discontinuity of a func-
tion. His terms were unique; however, his presen-
tation was rigorous. The lectures were lithographed
in 1906–1907 and republished in 1923 [Sh2]. G. M.
Fichtenholz, D. A. Kryzhanovsky, and I. V. Arnold
were among his students. One could unquestion-
ingly see the effect of this course in “Fundamen-
tals of Analysis” by G. M. Fihtenholz (1888–1959)
who attended Shatunovsky’s lectures and gradu-
ated from Novorossiysky University in Odessa in
1911.
Shatunovsky demonstrated an amazing scientific
undersense choosing works to be translated. He was
the first to translate Dedekind’s “Stetigkeit und ir-
rationale Zahlen” (written by Dedekind in 1872 and
translated by Shatunovsky in 1894) [DR] and Cantor’s
“Ueber eine Eigenschaft des Inbegriffes aller reellen
algebraischen Zahlen” (written by Cantor in 1874 and
translated by Shatunovsky in 1896) [Sh1]. It was in
these two works that a new concept of a number was
created to form basis for the 20th century mathemat-
ics.
From 1886 to 1917, there was a journal pub-
lished in Odessa, “Bulletin of Experimental Physics
and Elementary Mathematics” (Vestnik opytnoy fiziki
i elementarnoy matematiki). In 1896, they published
an article of O. S. Shatunovsky in issue 233 enti-
tled “Proof of Existence of Transcendental Numbers
(as per Cantor)” [Sh1]. Shatunovsky had laid down
the proof of theorems from Cantor’s work of 1874,
“Ueber eine Eigenschaft des Inbegriffes aller reellen
algebraischen Zahlen”, having added a description
of his more recent achievements, in particular, the
concept of power set, which appeared only in 1878
in Cantor’s work “Ein Beitrag zur Mannigfaltigkeit-
slehre”.
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Moscow, 1900. B. K. Mlodzeewsky
Boleslaw K. Mlodzeewski (1858–1923).
Owing to the acquisition of literature and re-
search travel, Moscow mathematicians were aware of
West-European scientific achievements. To obtain the
Master’s Degree, students used to attend lectures at
German and French research centres for at least one
term. Lectures given in Moscow University included
information on scientific achievements. The theory
of real variable functions was read by Boleslaw Ko-
rnelievich Mlodzeewsky (1858–1923). Owing to the
theory of sets, the course of mathematics and the-
ory of functions in the first place was rearranged on
other basis. Mlodzeewsky used the course of Ulisse
Dini as a base. Ulisse Dini used Cantor’s results in his
course as early as in 1870s [DU]. Mlodzeewsky gave
his course in the autumn term of 1900 and thereafter
gave it a couple of times until 1908 [M].
Notes of Mlodzeewsky’s lectures delivered in
1902 were found in archives of P. A. Florensky, the
then third-year student of the Department of Math-
ematics. The course included 29 lectures (three lec-
tures a week). Based on the lecture notes, F. A.
Medvedev supposed that “Mlodzeewsky did not seem
to be directly familiar with G. Cantor’s works at
that time. The name and numerous set-theoretic and
function-theoretic results of the latter were repeat-
edly mentioned in the lectures. However, judging
from the nature of this mentioning (lack of direct ref-
erences to Cantor’s works or clarifications to the ef-
fect that certain considerations were set forth based
on one of the above-listed works, etc.), it is reason-
able to suppose that by 1902, B. K. Mlodzeewsky had
learnt of Cantor’s work second-hand, mainly from
works of P. Tannery, G. Tannery, and A. Schoen-
flies” [M, p. 134]. The theory of sets is used in
Mlodzeewsky’s lectures to present the theory of func-
tion argument. He considered point sets (“clusters
of points”) and functions on the sets; he introduced
the concept of a limiting point and cluster set; clas-
sified sets into first and second kind; formulated
a theorem stating that a measure of a set of the
first kind equals zero; the upper and lower limit,
the concept of power of sets, countability of ratio-
nal and polynomial numbers; equipotency of various
dimensions continua, denumerability of a countable
sum of countable sets; uncountability of continuum
with reference to the continuum hypotheses; perfect
sets; ordinal type (“breed”); well-ordering (a “well-
organized group”); transfinite numbers and alephs
[M, p. 138–139].
Moscow, 1904. P. A. Florensky
Pavel A. Florensky (1882–1937).
Pavel Alexandrovich Florensky (1882–1937), a
prominent philosopher, theologian and priest later
shot dead, was from 1900 to 1904 a student of
the Department of Mathematics of Moscow Univer-
sity. In the autumn term of academic year1902/03,
he attended a course of Mlodzeewsky’s lectures
where he learnt of Cantor’s theory of sets. Since
1903, Florensky was working on his thesis entitled
“The Idea of Discontinuity as an Element of Out-
look” a preamble to which was published in 1986 in
Istoriko-matematicheskie issledovania. [FP1]. Floren-
sky writes about Cantor’s representation of continu-
ity.
Florensky turned to Cantor’s theory for a sec-
ond time in 1904 in his work entitled “Symbols of
Eternity (A Sketch of Cantor’s Ideas)” [FP2]. Floren-
sky made it his crusade to paraphrase the meaning
of Cantor’s works. He described the development of
definitions of potential and actual continuity in his-
tory of philosophy and continued with description of
Cantor’s theory of cardinals. However, he basically
addressed Cantor’s most recent works he wrote to
provide a philosophical underpinning of his under-
standing of the continuity and theory of kinds: “Ue-
ber die verschiedenen Standpuncte in bezug auf das
Actuelle Unendliche” (1886) and “Mitteilungen zur
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Lehre vom Transfiniten” (1888). Cantor’s theory, al-
though in a concise form, was set forth appropri-
ately. Basically, it was a paraphrase of the two articles
named above. Florensky focused on the philosophical
aspect of the theory more inclined to philosophy of
religion. He gave Cantor credit for the introduction
of actual infinity symbols. Further Florensky tried to
understand Cantor’s scientific motivation the back-
ground whereof he searched for in Cantor’s biogra-
phy, although he himself admitted that “Cantor’s bi-
ographic information has never been published and
therefore, facts are extremely scarce. So one has to
interpolate intuitively. However, having created a vi-
sion of Cantor’s personality of one’s own, it becomes
extremely difficult to prove the rightfulness of one’s
own vision.” [FP2, p. 120, emphasis as in the origi-
nal].
Florensky attributed the determination and pur-
poseful nature of Cantor’s scientific track to Jewish
religiosity enhanced to self-sacrifice. We may make an
allowance for the young age of Florensky who was but
twenty-two when he started interpolating or rather
imaging his views (and those of Vl. Soloviev) on the
inner world of a scientist he did not know, confusing
the ideas of ethnicity and religious affiliation. Now
we already know that Cantor was Lutheran born to
a family of Lutheran father and Catholic mother; that
it was merely his agnate grandfather who was Jewish,
and in the next generation his father, brother and sis-
ter were Lutheran, and one of his father’s other sisters
was Orthodox Christian. His male line goes up to Por-
tuguese Jews who settled in Copenhagen; his female
line goes up to Austrian Czechs and the Hungarians
who were Catholic [Si1, Si2]. With parents belonging
to different confessions, Georg Cantor was not very
religious and later, he consulted only Catholic theolo-
gians in search for a theological substantiation for
concepts of his theory, although appealed on a point
of all philosophic literature devoted to issues of eter-
nity and continuum.
Florensky believed that one can comprehend the
reality in symbols [FP2, p. 126] and therefore absol-
utized Cantor’s aspiration to create transfinite sym-
bols. “Whereas Cantor as an individual is a most real-
life image of a Jew, his philosophy is pretty much the
same.” [FP2, p. 127]. Confusing ethnic and religious
characteristics again, Florensky concluded that this
was the reason why Cantor considered the actual in-
finity: “The idea of a complete infinity for both the
absolute individual, the God, and for a human is the
domain of Jewry, and this idea seems to be the most
material grounds for Cantor. Meanwhile, others, the
Aryans, acknowledge only potential infinity, “bad”,
indefinite and infinite, the very thought of nonexis-
tence of the actual infinity seems unmerciful to his
sole.” [FP2, p. 127].
Having graduated from the University, Florensky
entered the Moscow Ecclesiastical Academy to be-
come a priest.
II
By the first decade of the 20th century, Cantor’s
theory had spread in mathematic community of Eu-
rope and Russia. On the basis thereof, the theory of
measure originated in works of Borel, Lebesgue, and
Baire. In 1911, the school of the theory of functions
and thereafter, the school of descriptive set theory
started to form in Moscow. D. F. Egorov and N. N.
Luzin were among their originators.
Kazan, 1904–1908. A. V. Vasiliev
Alexandre V. Vasiliev (1853–1929).
Since 1874, having graduated from Peters-
burg University, Alexandre Vasilievich Vasiliev
(1853–1929) worked at Kazan University first as
a privat-docent and from 1887, as a professor.
His broad education, proficiency in languages, and
numerous contacts with foreign scientists enabled
him to make a good organizer and enlightener. He
engaged in both research and socio-political activity,
and advocated Lobachevsky’s ideas having prepared
his collected works edition for publication. Georg
Cantor’s uncle, Dmitry Ivanovich Meyer (1819–1856),
famous lawyer and creator of Russian civil law [Si1],
worked in Kazan until 1855. There were two portraits
in Vasiliev’s study: a portrait of Lobachevsky and
that of Meyer. Vasiliev knew Cantor from letters they
exchanged and advocated his ideas.
From 1904 to 1908, A. V. Vasiliev’s “Introduc-
tion into Analysis” was published in the publishing
office of Kazan University to set forth principles of
the theory of sets. According to S. S. Demidov, “Lit-
tle by little, courses of analysis started to shape into
the present-day courses of the kind. Mathematicians
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from Odessa (S. O. Shatunovsky), Kiev (B. Y. Bukreev),
and Kazan (A. V. Vasiliev) were the first to do so” [DS,
p. 77].
Cantor’s theory was about 30 years of age by
1907. Over this time, works of his successors and crit-
icism of opponents enriched the theory and thus fi-
nally shaped it. However, 10 basic Cantor’s articles
made the entire theory. The first summary mono-
graph of Schoenflis appeared in 1900. However, this
one was not complete either. The theory had to be
presented in its entirety.
Cantor’s theory of sets included two parts: the
theory of linear point sets and theory of transfi-
nite numbers. Mlodzeewsky set the task of com-
prehensive presentation of the theory to two of
his candidates: V. L. Nekrasov and I. I. Zhegalkin.
Nekrasov was supposed to present the theory of point
sets in detail and Zhegalkin, the theory of transfi-
nite numbers. Each had to add results of his own
to the presentation. Both candidates met the chal-
lenges.
Zhegalkin defended his thesis on 12 March, and
Nekrasov, on 4 October. Their Master’s theses had
been published a year earlier to become the Russia’s
first monographs in the theory of sets.
Moscow-Tomsk, 1907. V. L. Nekrasov
Vladimir L. Nekrasov (1864–1922).
Vladimir Leonidovich Nekrasov (1864–1922)
graduated from Kazan University where he stayed
to work as a teacher. However, in 1900 he was
transferred to the newly formed Tomsk Institute
of Technology, Department of Abstract Mathemat-
ics. In order to prepare the Master’s dissertation, in
1902–1903 he stayed in Europe on academic mission.
His Master’s dissertation entitled “The Geometry and
Measure of Linear Point Domains”1was published in
1907 in “News-Bulletin of Tomsk Institute of Tech-
nology” (Izvestija Tomskogo Technologicheskogo
Instituta) [N].
Chapter 1 contained a detailed historical sketch
of basic results of the theory of sets and theory of
measure, and an exhaustive bibliographical review.
Before “Einleitung in die Mengenlehre” by A. Fraenkel
appeared in 1919, Nekrasov’s bibliography was the
most complete. The list of references was arranged
chronologically from 1638 to 1907. In the third chap-
ter entitled “The Most Recent Works”, Nekrasov sup-
plemented this list with references to works, which
had appeared by the time the manuscript of the third
chapter went to press. Nekrasov was trying to sep-
arate the theory of point sets from that of abstract
sets: “As far as the size is concerned, already Can-
tor found that point ranges may be finite, countable,
or have the size of continuity. Finding out relation
of the latter size within the series of alephs is the
task of the theory of transfinite numbers which is
none of our interest here” [ibid., p. 98]. Starting to
review history from discovery of infinitely small by
Newton and Leibniz, Nekrasov wrote “Bolzano was fa-
ther of contemporary theory of domains. However, it
was G. Cantor who developed and made it strictly sci-
entific.” [ibid., p. 2, emphasis as in the original]. In the
third chapter, Nekrasov supplemented the number
with precursors and Galileo with his example show-
ing the correspondence of infinite sets of a natural
number and their squares [ibid., p. 225]. Nekrasov
laid emphasis on concepts of a limiting point and
arbitrary set introduced by Cantor as fundamen-
tal. Further, he gave basic provisions of the theory
of point sets and named the three basic character-
istics of linear domains: size, structure, and mea-
sure.
The second chapter contained Nekrasov’s own re-
sults related to the geometry of linear sets which cor-
respond to the three types of deployment and combi-
nations thereof for both closed and open sets. The
structure of point of discontinuity of functions is
Nekrasov’s applied results. We can’t but mention that
Nekrasov was perhaps the first to note Ulisse Dini’s
priority in classification of the points of discontinu-
ity [ibid, p. 102]. The third chapter was supplemented
with new references and historical ordering of the de-
velopment of the set theory ideas. The fourth chap-
ter provided the measure theory of A. Lebesgue and
W. Young, although Nekrasov took out the beginning
of the measure theory from Riemann and Hankel.
Nekrasov noted that Cantor’s theory has been rec-
ognized: “The right to exist and the role of the the-
ory of domains within the general system of science
1Nekrasov’s “domain” shall be understood as a set.
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has been established: this theory is reckoned and now
its effect cannot be avoided quite in a number of
branches of analysis. And this entire evolution hap-
pened within some 30 years, let alone so-to-say its
prehistoric period.” [ibid., p. 97].
Owing to the thorough historical analysis, elab-
orate presentation of Cantor’s theory of point sets,
and Nekrasov’s own results, the monograph remains
significant to the present day.
Moscow, 1907. I. I. Zhegalkin
Ivan I. Zhegalkin (1869–1947).
Having graduated from Moscow University, in
1906–1907 Ivan Ivanovich Zhegalkin (1869–1947)
held a course in abstract set theory; in 1907 pub-
lished his monograph entitled “Transfinite Numbers”
[Z], and in 1908 defended his Master’s dissertation
with the same title. Thereafter he headed research
in mathematical logic where he obtained substantial
results, having connected classic logic and residue
arithmetic modulo 2. The residue ring modulo 2 is
used to be called Zhegalkin algebra. In his subsequent
works he proved monadic predicate calculus solvabil-
ity.
Zhegalkin presented Cantor’s algebra of transfi-
nite numbers in his dissertation in his own way, de-
ductively. There was no list of references, but for a
couple of references to works of Cantor, Dedekind,
Zermelo, and Bernstein. He mainly provided a trans-
formed presentation of Cantor’s last article of 1897
entitled “In support of the theory of transfinite sets”.
Zhegakin’s presentation of the preamble was differ-
ent. He thus hoped to avoid those contradictions in
the theory which had come to light by the start of the
20th century and were associated with the problem of
well-ordering and Zermelo theorem. Zhegalkin added
more stringent arguments to Cantor’s proof. He de-
serves credit for the statement regarding indepen-
dence of the problem of choice from all other mathe-
matic axioms made by him long before Serpinsky and
Goedel.
In the first chapter, Zhegalkin tried to build a
theory of cardinal and ordinal numbers before in-
troducing the concept of finite and infinite. He in-
troduced the concept of a finite set, ordering, and
well-ordering; concept of a sum, product, and map-
ping of sets; and his own concept of a “not genuine”
set. In the second chapter, he considered relation
of equivalence, power (as a cardinal number), addi-
tion, multiplication operations, and raising to power,
and this was the end of the theory of powers. The
third and fourth chapters were devoted to the con-
cept of an ordered set and concept of a type, and
their respective properties. The fifth chapter consid-
ered a completely ordered set and Zermelo theorem
(“every set can be thought as a well-ordered set”).
Zhegalkin proved the possibility to order the family
of sets for the case of disjoint sets (Zhegalkin calls
them “detached”). The sixth chapter studied prop-
erties of ordinal numbers, i.e. types of completely
ordered sets. Only after the theory of cardinal and
ordinal numbers had been built, he considered fi-
nite sets and numbers in the seventh chapter; in the
eighth chapter, he extracted countable sets there-
from as sets of all finite numbers. In the ninth chap-
ter, he introduced congruence of powers; Chapters
Ten and Eleven studied general properties of types
of countable sets (the numbers of a second class,
according to Cantor). The twelve’s chapter was de-
voted to forming of a scale of alephs, thirteenth chap-
ter studied the power of potency. Zhegalkin proved
König’s theorem for uncountable case. The mono-
graph ended with a list of paradoxes known by that
time.
In fact, Zhegalkin made an attempt to build a con-
sistent and complete transfinite number theory. How-
ever, he was based on the concept of a finite set with-
out strictly defining it. He also studied numbers that
were above class II, which was missing in Cantor’s
works.
Moscow School of the Theory of Functions and Sets
In 1910, D. F. Egorov launched a workshop in
Moscow University in the Theory of Functions. In
1911, the history of Moscow School of Set The-
ory started with Egorov’s theorem of uniform con-
vergence. This School was headed by Egorov and
N. N. Luzin. Luzin’s research created a new line,
descriptive set theory; research of his students de-
veloped numerous lines based on the set theory:
the theory of measure, set-theoretic topology, func-
tional analysis, the theory of probability, and many
other.
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III
Petersburg-Odessa, 1914. P. S. Yushkevich
Pavel S. Yushkevich (1873–1945).
Three basic works of Cantor already translated
(not paraphrased) were published in 1914. From
1913 to 1915, Vasiliev was publishing series enti-
tled “New Ideas in Mathematics” in Petrograd. To
have Cantor’s works translated, he engaged a philoso-
pher and translator of philosophic literature, Pavel
Solomonovich Yushkevich (1873–1945), father of
Adoph Pavlovich Yushkevich. He translated three of
the most characteristic works of Cantor which con-
tained the quintessence of his theory: “Grundlagen
einer allgemeinen Mannigfaltigkeitslehre”, “Ueber die
verschiedenen Standpuncte in bezug auf das Actuelle
Unendliche”, and “Mitteilungen zur Lehre vom Trans-
finiten”[C1].
We say almost nothing here about personal con-
tacts of Russian scientists with Cantor. We would only
mention that Cantor was elected foreign member of
Kharkov Society of Mathematicians.
Cantor’s theory as it had originally appeared
(a naïve theory of sets) was revised to make ba-
sis for new lines in the theory of functions, theory
of measure, functional analysis, set-theoretic topol-
ogy, and many other branches of mathematics. Cer-
tain Russian mathematicians addressed directly fun-
damentals of the theory of sets. Let us mention a
Chuvash mathematician, Isaya Maximovich Maximov
(1889–1976) among them. He was a post-graduate
student of Luzin, dealt in the theory of sets, the-
ory of numbers, theory of functions, and studied
the concept of transfinite space created by him in
1930s.
Moscow-Novosibirsk, 1968. A. I. Fet. Dramatic Fate
of the First Complete Translation of Cantor into
Russian
The story I am about to tell was imparted to me
in June 2014 by Liudmila Pavlovna Petrova, widow of
A. I. Fet, the first translator of all Cantor’s works. Now
she lives in Novosibirsk.
Abram I. Fet (1924–2007).
Abram Ilyich Fet (1924–2007), mathematician,
philosopher, opinion journalist, and brilliant transla-
tor, was born in Odessa and graduated from Tomsk
University. In 1948, he defended his Candidate Thesis
in Moscow. His research advisor was L. A. Lusternik.
In 1967, he successfully defended his Ph.D. thesis,
which contained the currently known result: Fet’s the-
orem about two geodesics. Since 1955, he had worked
in Novosibirsk. That’s what Liudmila Pavlovna told
me (the fragments of her letter are published with her
consent):
“Whereas you deal with Cantor and history at
large, it will probably be interesting for you to know
about one episode from history of Cantor’s her-
itage in Russia. A. I. Fet translated not only Can-
tor’s biography written by Frenkel, but all his works.
The translation he had done was that of the fol-
lowing publication: Georg Cantor, Ernst Zermelo,
ed., Gesammelte Abhandlungen mathematischen und
philosophischen inhalts, mit erläuternden anmerkun-
gen sowie mit ergänzungen aus dem briefwechsel
Cantor-Dedekind, Berlin, Verlag von Julius Springer,
1932.
This publication included almost all works writ-
ten by Cantor. Furthermore, there were five letters in
the appendix from those Cantor and Dedekind had
wrtten to each other, and Cantor’s biography written
by Frenkel.
He translated those works in 1969–1970 to earn
some money, as in autumn 1968 A. I. Fet was sacked
after he had signed a letter in defence of illegally
convicted and remained unemployed till summer of
1972.
DECEMBER 2015 NOTICES OF THE ICCM 7
PROOF 2016-02-10
The Contract for the translation was signed with a
Moscow publishing house, “Fizmatlit”, in the name of
A. V. Gladky, as A. I. was debarred from employment.
When the translation was already ready and the pub-
lishing house started working on the book, the book
was rejected by the commission of Pontryagin (not
the translation, Cantor’s book itself!).”
L. S. Pontryagin
In 1970, L. S. Pontryagin (1908–1988), academi-
cian who had made a great contribution in topology
and variations calculus, headed a group created by
him to form part of a section of the editorial review
board at the Academy of Sciences in the USSR, Chief
Editorial Board of Physico-Mathematical Literature at
NAUKA Publishing House. This is what he himself
wrote: “Already before the group was formed, the sec-
tion had resolved to have G. Cantor’s collected works
translated into the Russian language. When this res-
olution was put to vote of the section a second time,
this issue got to the group. Before the group started
considering it, I. R. Shafarevich met me in the can-
teen and said: “I do not seem to be a member of the
section anymore2and therefore would like to warn
you regarding the collected works of Cantor. Creation
of the theory of sets is unduly assigned to Cantor in
whole. In fact, quite a large amount of the work was
done by Dedekind. This can be seen in letters Can-
tor and Dedekind exchanged. Therefore, these letters
should be enclosed with Cantor’s work.”
I started thinking over this suggestion of Shafare-
vich and concluded that Cantor’s works should not be
published at all, as it is unreasonable to attract atten-
tion of young mathematicians to the theory of sets at
the moment.
Very popular in Luzin’s times, currently the the-
ory of sets has already lost the edge. The group ac-
cepted my suggestion, and the book was rejected. The
section readily agreed with us regardless the fact that
Cantor’s works had already been translated! So we
had to pay for the translation services.” [P, p. 175].
Liudmila Pavlovna Petrova added:
“Lev Semenovich was mistaken, the translation ser-
vices have never been paid for.
The typewritten text of the translated works on 536
pages is kept in our home archives. All formulas,
insertions, and colour markings for the publishing
house were handwritten by A. I. Fet.
When in 1985 F. A. Medvedev and A. P. Yushke-
vich3translated Cantor’s works for NAUKA Pub-
lishing House they were not aware of the existence
of the already completed translation of Fet (or A. V.
Gladky).”
2Shafarevich was expelled from the section as a result of a
conflict with Pontryagin, the fact whereof was described by
Pontryagin.
3A. P. Yushkevich was an editor, but not a translator.
E. Savenko wrote about Fet’s expertise as a trans-
lator as follows:
“The scientist was concerned about the issue of
translations his whole life. In 1997, speaking at the
conference devoted to this issue, Fet noted that in
1960s, “the epoch of illiterate translations started”
[FA]. He believed that the reasons for that were in
the loss of skills of selecting of books to be trans-
lated and poor competency of translators, that is
to say, their inability to understand the essence
of the text being translated caused by poor aca-
demic training rather than poor knowledge of the
language. A. I. Fet himself, an erudite and a person
of keen intellect, possessed unique skills neces-
sary to do quality translations: he would promptly
perceive all significant ideas and appropriately lay
them down.” [S].
L. P. Petrova added: “He told me that, in his opin-
ion, a good translation of a book in math is a trans-
lation which would make this book better. A. I. him-
self looked upon such translation work as a chance
to take a good look at the book he was interested in.”
Author’s remark: I translated the first biography
of Cantor written by A. Fraenkel from the German lan-
guage. However, when I saw the book translated by
A. I. Fet, I was carried away by his lucid and vigorous
style that made the text full-blooded and emotional
without distorting the original a single iota. Trans-
lators would understand me. I believe that Cantor’s
works translated by Fet should have been published
as well, although we already have a very good trans-
lation of 1985 at our disposal.
Moscow-Leningrad, 1985. F. A. Medvedev
Fedor A. Medvedev (1923–1994).
In February 1983 Cantor’s works were ready for
publication, and in 1985 they were published by
NAUKA Publishing House [C3]. The publication was
prepared by Academician Kolmogorov (1903–1987)
and a renowned math historian A. P. Yushkevich
(1906–1993). The publication included his basic
works in the theory of sets, letters Cantor and
8 NOTICES OF THE ICCM VOLUME 3, NUMBER 2
PROOF 2016-02-10
Dedekind exchanged, and E. Zermelo’s notes to the
German publication. The underlying source text was
the publication of 1932 edited by Zermelo [C2]. Un-
like Zermelo’s publication which included five let-
ters of those Cantor and Dedekind wrote to each
other, the Russian publication of 1985 includes Can-
tor’s works translated by F. A. Medvedev and 49
letters of the above mathematicians regarding the
German publication of E. Noether and G. Cavaillès
[B].
The Russian publication of 1985 [Cantor, 1985]
includes the three Cantor’s articles as mentioned
above translated by P. S. Yushkevich and published in
1914 in the collection of works entitled “New Ideas in
Mathematics”; eleven articles translated by Fedor An-
dreevich Medvedev, including “Principien einer The-
orie der Ordnungstypen. Erste Mitteilung” which was
not included in the collection of 1932. It was found by
A. Grattan-Guinness as a manuscript kept in Mittag-
Leffler Institute in Sweden and published by him in
1970 [G]. This article was written by Cantor in 1884
for Acta Mathematica, however, it was rejected by
Mittag-Leffler as too philosophic.
Fedor Andreevich Medvedev (1923–1994), math-
ematician and math historian, author of four books
and numerous articles in the history of the theory of
sets and work of Cantor himself, devoted his whole
life to history of mathematics. Not only did he thor-
oughly translate Cantor’s works, letters he exchanged
with Dedekind, and Zermelo’s comments, he also
added his very valuable notes to Cantor’s works. Fe-
dor Andreevich was my teacher; it is thanks to him
that I started to study the history of Cantor’s the-
ory.
The fate of Russian translations of Cantor’s
works has lived its 20th century history together with
Russia. People who touched Cantor’s heritage were
remarkable, and their names have come down in the
history of Russian mathematics.
References
[B] Briefwechsel Cantor-Dedekind. 1937 / Hrsg. Von E.
Noether, J. Cavaillès. Paris.
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[C2] Cantor, G., 1932. Gesammelte Abhandlungen mathe-
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10 NOTICES OF THE ICCM VOLUME 3, NUMBER 2
ResearchGate has not been able to resolve any citations for this publication.
Uchenie o mnozhestvach Georga Cantora (Set theory by Georg Cantor) // Novye idei v matematike (New ideas in mathematics)
  • G Cantor
Cantor, G., 1914. Uchenie o mnozhestvach Georga Cantora (Set theory by Georg Cantor) // Novye idei v matematike (New ideas in mathematics). Under the editorship of A. V. Vasiliev. St.-Petersburg.
Trudy po teorii mnozhestv (Colected works on Set Theory). Seria "Klassiki nauki
  • G Cantor
Cantor, G., 1985. Trudy po teorii mnozhestv (Colected works on Set Theory). Seria "Klassiki nauki". Moskva: Nauka.
Samuil Osipovich Shatunovsky // Uspechi matematicheskich nauk. VII
  • N Chebotarev
Chebotarev, N., 1940. Samuil Osipovich Shatunovsky // Uspechi matematicheskich nauk. VII, 315-321.
Russkie matematiki v Berline vo vtoroj polovine XIX -nachale XX veka (Russian mathematicians in Berlin in the second part XIX -the beginning of XX). -Istoriko-matematicheskie issledovania
  • S Demidov
Demidov, S., 2000. Russkie matematiki v Berline vo vtoroj polovine XIX -nachale XX veka (Russian mathematicians in Berlin in the second part XIX -the beginning of XX). -Istoriko-matematicheskie issledovania. Moskva: Janus-K. -5 (40), 71-83.
Fondamenti per la teoria delle funzioni di variabili reali. Pisa: tip. Nistri
  • U Dini
Dini, U., 1878. Fondamenti per la teoria delle funzioni di variabili reali. Pisa: tip. Nistri.
Polozhenie s perevodami v Rossii (A situation with translating in Russia). A lection on the discussion
  • A Fet
Fet, A., 1997. Polozhenie s perevodami v Rossii (A situation with translating in Russia). A lection on the discussion "Science, Education and Open Society", Soros Foundation. Novosibirsk, 15.10. 1997. http://modernproblems.org.ru/press/259-2014-07-21-07-25-37.html.
Idea of discontinuity as an element of world outlook") // Istoriko-matematicheskie issledovania. Moskva: Nauka
  • P Florensky
Florensky, P., 1903. Vvedenie k dissertazii "Ideia preryvnisti kak element mirosozertsania" (Introduction to thesis "Idea of discontinuity as an element of world outlook") // Istoriko-matematicheskie issledovania. Moskva: Nauka. 1986. XXX. 159-177.