UREM-ULB :
Unité de Recherche sur l’Enseignement des Mathématiques

Hommage à Vladimir Arnold (1937-2010)
dans les Notices

Tribute to
Vladimir Arnold by
Boris Khesin and Serge Tabachnikov,
Coordinating Editors

Quelques extraits

 Q : How did you become a mathematician ? What
was the role played by your family, school, mathematical
circles, Olympiads ? Please tell us about
your teachers.
 A : I always hated learning by rote. For that
reason, my elementary school teacher told my
parents that a moron, like myself, would never
manage to master the multiplication table.
My first mathematical revelation was when I
met my first real teacher of mathematics, Ivan
Vassilievich Morozkin. I remember the problem
about two old ladies who started simultaneously
Vladimir Igorevich Arnold
from two towns toward
each other, met
at noon, and who
reached the opposite
towns at 4 p.m.
and 9 p.m., respectively.
The question
was when they started
their trip.
We didn’t have algebra
yet. I invented
an “arithmetic” solution
(based on a scaling—
or similarity—
argument) and experienced
a joy of discovery ;
the desire to
experience this joy
again was what made me a mathematician.

 Q : You spend much time popularizing mathematics.
What is your opinion about popularization ?
Please name merits and demerits of this hard
genre.
 A:One of the very first popularizers, M. Faraday,
arrived at the conclusion that “Lectures which
really teach will never be popular ; lectures which
are popular will never teach.” This Faraday effect is
easy to explain : according to N. Bohr, clearness and
truth are in a quantum complementarity relation.

 Q : Many readers of Kvant aspire to become
mathematicians. Are there “indications” and “contraindications”
to becoming a mathematician, or
can anyone interested in the subject become one ?
Is it necessary for amathematician-to-be to successfully
participate in mathematical Olympiads ?
 A : When 90-year-old Hadamard was telling
A. N. Kolmogorov about his participation in
Concours Général (roughly corresponding to our
Olympiads), he was still very excited : Hadamard
won only the second prize, while the student
who had won the first prize also became a
mathematician, but a much weaker one !
Some Olympiad winners later achieve nothing,
and many outstanding mathematicians had no
success in Olympiads at all.
Mathematicians differ dramatically by their time
scale : some are very good tackling 15-minute
problems, some are good with the problems that
require an hour, a day, a week, the problems
that take a month, a year, decades of thinking.
A. N. Kolmogorov considered his “ceiling” to be
two weeks of concentrated thinking.
Success in an Olympiad largely depends on
one’s sprinter qualities, whereas serious mathematical
research requires long distance endurance
(B. N. Delaunay used to say, “A good theorem takes
not 5 hours, as in an Olympiad, but 5,000 hours”).
There are contraindications to becoming a research
mathematician. The main one is lack of
love of mathematics.

Commentaire d’Hugues Vermeiren

Une controverse en pleine guerre froide : Arnold, Pontriagine et Margulis (Fields 78) :
 http://mathoverflow.net/questions/27144/why-didnt-vladimir-arnold-get-the-fields-medal-in-1974

Pontriagine, aveugle à 14 ans, a écrit une autobiographie, disponible en Russe et en ligne :
 http://www.ega-math.narod.ru/LSP/book.htm