MATHEMATICS AS A PROFESSION IN THE USSR

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000700180455-6
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 4
• Document Creation Date: December 22, 2016
• Document Release Date: September 6, 2011
• Sequence Number: 455
• Publication Date: June 4, 1954
• Content Type: REPORT

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STAT
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MATHEMATICS AS A PROFESSION IN THE USSR
Wisaenschaftliche Annalea,
Vol II, No 12, pp 77 _Y79
Berlin, Dec 1953
[Comment: Andrey Nikolayevi~:z Kolmogorov (1903- ) has been a
professor at Moscow University since l~bl; an Academician since 19k5,
a member of the Division of Mathematical Statistics sinc~1948, and
one of the most prominent Soviet mathematicians. Source for the
following is a German rendition of an article in the Soviet peri-
odical Sovetska? Nauka, Moscow, 1952.1
Obviously mathematics is important in mechanics, physics, and astronomy.
Mathematics is equsll;i important in the practices 1 work of engineers and tech-
nical personnel. $owever, the selection of mathematics as a profession is
not a simple one.
}dost peonle imagine t~~t mathematical textbooks and handbooks contain
sufficient rules and formulas to solve anv practical problem. Even educated
people wonder if it is aocsile to discover any~izing new ir. mathematics.
Tire fundamentals of mathematics taught in school were discovered long
ago but this elementary 'rnowledge becomes useful only when the student learns
to derive it by himself. Therefore, students need teachers who not only know
their subject well, but also are ent}zusiastic about it and consider it a liv-
ing, growing subject.
It is even more important that men who intend to use mathematics in the
solution of technical problems possess the ability to find a new mathematical
aPProach; this is especially true of enrineez?s who perform mathematical com-
putations.
Since not every man };as the required mathematical s'rill and ability, most
of ou:? applied scientific-researc}: institutes and some of our big industrial
plants have begun to engzige specialized mathematicians who cooperate with their
engineers; but in many fields, unfortunately, mathematicians are still lacking.
Many problems require enormous comoutat.ional work surpassing individual human
capabilities, and mz:st be solved by our calculator bureaus, which are staffed
with ninny dozens of computers and which a:?e giving very good results. Stresses
of dams under elastic strains, filtration of water under dams, air resistance
in aerodynaaics or in ballistics are typical examples of problems in computa-
tion which keep our czlculator bureaus busy Por months and even years. This
often painfully detailed work requires compzters not only with experience, but
also with the requisite mathematical background.
Many of our mathematicians who possess creative initiative coupled with
thorough knowledge acquired in our universities are now endeavoring to present
mathematical problems in ^ form amenable to numerical solution with leas diffi-
culty than usual. The mathematical theory of computational methods is de-
veloping into a broad science, and the need for specialists who have mastered
these techniques increases with the development of machine computation. These
mathematicians arc often confronted wit}, the peculiar problem of "programing",
i.e., setting the computational procedure in a form suitable for automatic
processing by machines.
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theoretical foundations is basically falseCe Actually,dmathematicsoistcontinu-
ously being confronted with new ideas, new theories. New problems of mechanics
(nonlinear oscillations, mechanics of ultrasonic velocities) and of physics
(quantum physics) and related topics are introducing further developments into
mathematics.
Cn the other hand, after the accumulation of a certain number of special
problems and their particular solutions, new general theories are developed
which facilitate standardized methods for general solutions. For instance,
functional snalysis, which is related to mathematical analysis approximately
as algebra is related to arithmetic, is developing now, whereas mathematical
analysis was created in the 17th and 18th centuries and is regularly taught
at all higher educational institutions. The so-called operator technique of
functional analysis is already widely applied in modern physics and engineer-
ing.
During the first years of the October Revolution, our youth endeavored
to enter our technical schools, which they considered the gateway to partici-
pation in the socialistic reconstruction. later when scientific education
was urgently needed in the economic development of our country, it became
essential to overcome the diffidence, now r_liminated, of some youths tcward
universities. gut young stv9~nts rare still in awe o: mathematics, which they
regard as a dry and abstract science, more awesome than other sciences. Such
n notion should be refuted.
Cooperation between mathematicians and representatives of related fields
is now. closer than ever and becomes most fruitful if mathematicians do not
testrict themselves,+yo the solution of a problem, but trr to penetrate deeply
into the physical and technical meanings. The specialist in mathematical and
theoretical physics, in theoretical mechanics, or in theoretical geophysics
may be educated in two ways; he may stert his education with the study of
physics, mechanics, or geophysics; or lie may attend lectures at the mathe-
mstical~faculty of a university and simultr:neously work in his specific field.
The predominant opinion is that better results pre obtained by the second
method, because it is easier to study aerodynamics, gas dynamics, seismography,
and dynamic meteorology with a solid mathematical foundation. To some, such
a viewpoint seems exaggetated because, Tor example, mathematicians active in
related fields have rarely been able to master experimental techniques. Hr_
have to admit, however, that outstanding specialists in the naturc:l sciences
have come from the ranks of E:?adura ed mathematicians.
The common notion that special aptitude is needed for the study and com-
prehension of mathematics is an exaggerated one, tJevertheless, it is natural
to attempt to verify the student's mathematical abilities or, as it is often
expressed, "mathematical talent" before he selects mathematics as his pro-
fession.
Just what are these abilities? First, success in mathematics does not
depend completely on memorizing; facts, especially formulas. Anyone uho has
had some experience in handling algebraic computations and in using clever
transformations of complex formulas Y,nows that an adequate method of solution
may be round without the use of standard formulas. The finding of such u
method early marks the ability of :i mathematician for serious scientific work.
Second, the mathematician always endeavors as far as possible to illus-
trate geometrically the problems which he analyzes. Therefore, geometrical
representation or, as it is often called, "geometrical intuition," is an im-
portant ability in all branches of mathematics, even in the most abstract ones.
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, bhe abi~l~ty~'to makg deductive logical conclusions is another char-
acterietic'of?math~bical aptitude. The understanding oP the principle of
mathematical derivation and the ability to apply such principles correctly are
Bond criteria of maturi}y in logic, the necessary prerequisite of n mathema-
tician.
and integralr~alculus madecomplicatedtcomputationsewhichtpreviouslyfusedtial
elementary mathematics much simpler and easier. Differential equations sim-
plify the expression of laws governing celestial bodies moving under gravita-
tional action, of principles and operation of various radio-engineering
circuits of stress distribution in.mechnnical constructions, etc. Mathema-
ticians are expected to establish methods for the solution of such equations
by natural scientists and physicists.
In this article, we have been trying to clarify for the future mathematics
student the diversity of interests and aims of mathematical studies.
The need .for mathematicians in scientific and industrial research insti-
tutes.,, in related sciences (physics, geophysics), and in various fields of
modern engineering is co
ti
n
nuously growing.
Mathematicians in such institutes do not confine their operations to
guidance and execution of computations (as ir, calculator bureaus or statlons)
or to .the solution of mathemwtical problems presented by machinists, physi-
cists, or engineers, but specialize in their profession after a thorough
education in mathematics ns many fanous scientists have done (e.g., among the
etudenta'of Moscow University, one can name M. V. Keldysh and M. A. Iavrent'yev
in mechanics and A. N. Tikhnnno t? ? ,......._.__~
denerally speaking, the study of mathematics is the most important edu-
catioaal background for specialists in all fields of pure science and engi-
neering, since all These sciences require n modern mathematical apparatus.
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