Ilya Piatetski-Shapiro

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איליה פיאטצקי-שפירו

Born

30 March 1929

Died

21 February 2009

(aged 79)

, Israel

Alma mater

(

)

Known for

Awards

(1981)

(1990)

Scientific career

Fields

Institutions

Doctoral

students

Ilya Piatetski-Shapiro

(

איליה פיאטצקי-שפירו

;

Илья

Иосифович Пятецкий-Шапиро

Ilya Iosifovich

Pyatetsky-Shapiro

;

30 March 1929 – 21 February 2009) was a Soviet-born

Israeli mathematician. During a career that spanned 60 years he made major

contributions to applied science as well as

. In his last

forty years, his research focused on pure mathematics; in particular,

and

. His main

contribution and impact was in the area of

and

For the last 30 years of his life he suffered from

. With

the help of his wife Edith, he was able to continue to work and do mathematics

at the highest level, even when he was barely able to walk and speak.

Moscow years: 1929–1959

[

]

Piatetski-Shapiro was born in 1929 in

. Both his father,

Iosif Grigor'evich, and mother, Sofia Arkadievna, were from traditional Jewish

families, which had become assimilated. His father was from

, a

small city in

, with a largely Jewish population. His mother was from

, a similar small city in

. Both parents' families were middle-

class, but they sank into poverty after the October revolution of 1917. He

became interested in mathematics at the age of 10, struck, as he wrote in his

short memoir, "by the charm and unusual beauty of negative numbers", which his

father, a PhD in chemical engineering, showed him.

In 1952, Piatetski-Shapiro won the Moscow Mathematical Society Prize for a

Young Mathematician for work done while still an undergraduate at Moscow

University. His winning paper

contained a solution to the problem of the

French analyst

The award was especially remarkable because of the atmosphere of strong

in Soviet Union at that time.

[

]

Despite the award, and a very strong recommendation by his mentor

, a professor of mathematics at

and an important

member (Gelfond’s father was a friend of

), Piatetski-

Shapiro’s application to graduate program at Moscow University was rejected. He was ultimately admitted to the

, where he received his Ph.D. in 1954 under the direction of

. His early work

was in classical analytic number theory. This includes his paper on what is now known as the

Piatetski-Shapiro prime

number theorem

which states that, for 1 ≤

≤ 12/11, the number of integers 1 ≤

≤

for which the integer part

is prime is asymptotically

log

→ ∞.

After leaving the Moscow Pedagogical Institute, he spent a year at the

, where he received the

advanced Doctor of Sciences degree, also in 1954, under the direction of

. His contact with

Shafarevich, who was a professor at the Steklov Institute, broadened Piatetski-Shapiro's mathematical outlook and

directed his attention to modern number theory and algebraic geometry. This led, after a while, to the joint paper

in which they proved a

for

Moscow years: 1960s

[

]

Piatetski-Shapiro in 1958 was made a professor of mathematics at the Moscow Institute of Applied Mathematics, where he

introduced

. By the 1960s, he was recognized as a star mathematician. In 1965 he was appointed to an

additional professorship at Moscow State University. He conducted seminars for advanced students, among them

(now at Yale) and

(now at Hebrew University). He was invited to attend the 1962

in Stockholm, but was not allowed to go by Soviet authorities (Shafarevich, also invited,

presented his talk). In 1966, Piatetski-Shapiro was again invited to the ICM in Moscow

where he presented a 1-hour

lecture on Automorphic Functions and arithmetic groups (Автоморфные функции и

арифметические группы).

Piatetski-Shapiro was not allowed to travel abroad to attend meetings or visit colleagues except for one short trip to

Hungary. The Soviet authorities insisted on one condition: become a party member, and then you can travel anywhere you

want. Ilya gave his famous answer: “The membership in the Communist Party will distract me from my work.”

During the span of his career Piatetski-Shapiro was influenced greatly by

. The aim of their

collaboration was to introduce novel representation theory into classical modular forms and number theory. Together

with Graev, they wrote the book

Automorphic Forms and Representations

Refusenik period and emigration to Israel

[

]

During the early 1970s, a growing number of Soviet Jews were permitted to emigrate to Israel. The anti-Jewish behavior

in the Soviet Union, however, was not enough to make Piatetski-Shapiro want to leave his country. What shook him to

the core was the difficulty of maintaining a Jewish identity and the enforced conformity to communism around him in

the scientific community. He didn’t wish this future for his son, sixteen at the time.

[

]

Piatetski-Shapiro lost his part-time position at mathematics department of Moscow State University in 1973, after he

signed a letter asking Soviet authorities to release a dissident mathematician

from a mental

institution. Many other mathematicians who signed the letter (including Shafarevich) also lost their part-time

positions.

[

]

After his ex-wife and son left the Soviet Union in 1974, Piatetski-Shapiro also applied for an exit visa to Israel and

was refused.

[

]

After applying for emigration in 1974, he lost his research position at the Moscow

Institute of Applied Mathematics (IPM). The authorities refused to grant him an exit visa, claiming that he was too

valuable a scientist to be allowed to leave. As a

, he lost access to mathematical libraries and other

academic resources. He continued his researches nevertheless, and colleagues took books from the library for

him.

[

]

As a prominent refusenik with connections to an international scientific community, Piatetski-Shapiro was followed

around by a KGB car and his apartment was under electronic surveillance. He conducted his meetings with friends and

colleagues by writing on a plastic board, especially when he needed to communicate about his situation. His plight as

a mathematician, with serious restrictions on his researches and without means for survival, attracted much attention

in the U.S. and Europe.

[

]

In 1976, a presentation was made to the Council of the National Academy of

Sciences urging the use of their good offices to get Piatetski-Shapiro an exit visa. Later that year, he obtained one.

His second marriage ended as his then-current wife remained in Moscow.

He visited colleagues all over the world who

had signed petitions and fought for his freedom before going to Israel. He was welcomed warmly upon arrival in Israel

and accepted a professorship at

. He was elected into

1978.

After leaving Soviet

Union, Piatetski-Shapiro also visited the USA in 1976 and spent a semester as a visiting

professor at

[

]

Yale and converse theorem

[

]

Starting in 1977, Piatetski-Shapiro divided his time between Tel Aviv University and

, directing

doctoral dissertations in both places. One of his major works at Yale dealt with the

which

establishes a link between

matrix groups and

[

]

For

= 1 this theorem is classical. The assertion for

= 2 was proved by

, and the novel version for

= 3

was conceived by Piatetski-Shapiro while he was still a refusenik in the Soviet Union.

It took another 25 years and

works with other collaborators, in particular his student

, before a full result for the general case was

completed.

The converse theorem has played a role in many of the results known in the direction of the

Last years

[

]

Piatetski-Shapiro battled

for the last 30 years of his life.

His condition worsened in the last 10

years to the point where he was barely able to move and speak, but thanks to the support of his wife Edith, he was

still able to travel to mathematical conferences.

With the help of James Cogdell he was able to continue research

until almost his last days.

[

]

He was married three times and had a son,

and daughters, Vera Lipkin and Shelly Shapiro

Baldwin.

[

]

Awards and honours

[

]

Piatetski-Shapiro was elected to the

in 1978,

was a Guggenheim Fellow for

the academic year 1992–1993,

and was the recipient of numerous prizes, including:

In 1981, the

, for mathematics;

and

In 1990, the

In 2020,

listed Piatetski-Shapiro as one of the Russian-speaking Jews who shaped Israel. It notes

that along with colleague James Cogdell, Piatetski-Shapiro developed the Converse Theorem, which finds some deep

relationships between different fields of mathematics.

He was invited to address the quadrennial

— one of the highest mathematical

honors — 4 times: 1962, 1966 (gave plenary address), 1978 (presented 45 minute talk), and 2002.