EMS Newsletter June 2010 - European Mathematical Society ...

Israel Moiseevich Gelfand
Vladimir Retakh
Israel Gelfand, a mathematician compared by Henri Cartan
to Poincare and Hilbert, died in New Brunswick, New Jersey,
USA, on 5 October 2009.
Israel Moiseevich Gelfand was born on 2 September 1913
in the small town of Okny (later Red Okny) near Odessa in the
Ukraine. There was only one school in town but Gelfand was
lucky enough to have a good and encouraging mathematics
teacher (one of his classmates David Milman also became a
mathematician). In 1923, the family moved and Gelfand entered
a vocational school for laboratory technicians. However,
he was expelled in the ninth grade as a son of a “bourgeois element"
– his father was a mill manager.
In his early years, Gelfand lived in total mathematical isolation.
The only books available to him were secondary school
texts and several community college textbooks. Through them,
he deepened his understanding of mathematics, jumping over
centuries of development. Like Ramanujan, he was experimenting
a lot. He was not, however, simply interested in solving
separate problems but also trying to understand how these
problems related.
From this period came his Mozartean style and his belief
in the unity and harmony of mathematics – the unity determined
not by rigid and loudly proclaimed programs but rather
by invisible and sometimes hidden ties connecting seemingly
different areas. Gelfand described his school years and mathematical
studies in an interview published in “Quantum", a
science magazine for high school students [1]. In this interview
he often repeats “Loser takes all" (the title of a Graham
Greene novel). In his own words:
It is my deep conviction that mathematical ability in most future
professional mathematicians appears . . . when they are 13 to 16
years old . . . This period formed my style of doing mathematics.
I studied different subjects but the artistic form of mathematics
that took root at this time became the basis of my taste in choosing
problems that continue to attract me to this day. Without
understanding this motivation, I think it is impossible to make
heads or tails of the seeming illogicality of my ways in working
and the choice of themes in my work. Because of this motivating
force, however, they actually come together sequentially and
logically.
At the age of 15 Gelfand learned of a series for calculating the
sine. He described this moment in the “Quantum" interview:
Before this I thought there were two types of mathematics, algebraic
and geometric . . . When I discovered that the sine can be
expressed algebraically as a series, the barriers came tumbling
down, and mathematics became one. To this day I see various
branches of mathematics, together with mathematical physics,
as parts of a united whole.
In 1930, sixteen and a half years old, Gelfand left his parents
and moved to Moscow to live with distant relatives. For a
while he did not have steady work and lived on earnings from
occasional odd jobs. At some point he had the good fortune to
work at the check-out counter at the Lenin Library. This gave
Israel Moiseevich Gelfand (Courtesy of Rutgers University)
Obituary
Gelfand a rare opportunity to talk with mathematics students
from Moscow University. From these contacts he learned that
none of his discoveries were new. Neither this nor other circumstances
of his life deterred him and his interest in mathematics
grew. He continued his intensive mathematical studies
and began attending seminars at Moscow University.
Just as in his abrupt expulsion from school, the next twist
in Gelfand’s fate was also one of many paradoxes of life in
the Soviet Union. On the one hand, as the son of a “bourgeois
element" he could not become a university student. On the
other hand, at 18 he was able to obtain a teaching position at
one of many newly created technical colleges and, at just 19,
to enter the PhD program at Moscow University. The reasons
are simple: the Soviet state needed knowledgeable instructors
to educate its future engineers and scientists with the proper
“proletarian origins". Furthermore, the system was not rigid
enough to purge or even strictly regulate graduate schools.
Therefore, Gelfand could enter a PhD program without a college
or even a high school diploma.
Gelfand was influenced by several Moscow mathematicians,
especially his thesis adviser A. N. Kolmogorov. In the
“Quantum" interview Gelfand said that from Kolmogorov he
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