Christos Papakyriakopoulos
Encyclopedia
Christos Dimitriou Papakyriakopoulos, commonly known as "Papa" (Χρήστος Δημητρίου Παπακυριακόπουλος in Greek
; born in Chalandri
, Athens
, Greece
on June 29, 1914, died on June 29, 1976, Princeton, New Jersey
), was a Greek
mathematician
specializing in geometric topology
. He worked in isolation at Athens University being awarded a Ph.D on the recommendation of Carathéodory. In 1948 he was invited by Ralph Fox
to come as his guest at the Princeton
mathematics department. Fox had been impressed by a letter from Papakyriakopoulos which purported to prove Dehn's lemma
. The proof, as it turned out was faulty, but Fox's sponsorship would continue for many years and enabled Papakyriakopoulos to work on his mathematics without concern of financial support.
Papakyriakopoulos is best known for his proofs of Dehn's lemma, the loop theorem
, and the sphere theorem
, three foundational results for the study of 3-manifold
s. In honor of this work, he was awarded the first Veblen Prize in Geometry
in 1964. From the early sixties
on, he mostly worked on the Poincaré conjecture
.
The following unusual limerick
was composed by John Milnor
, shortly after learning of several graduate students' frustration at completing a project where the work of every Princeton mathematics faculty member was to be summarized in a limerick:
The phrase "without any strain" is not meant to indicate that Papa did not expend much energy in his efforts. Rather, it refers to Papa's "tower construction", which quite nicely circumvents much of the difficulty in the cut-and-paste efforts that preceded Papa's proof.
He sympathized with leftist politics. When he went to live in the USA, the Greek authorities reported him to the American authorities as a "communist".
He was a reclusive character, spending most of his time in his office listening to his beloved Wagner. Legend has it that in the US he lived for 25 years in the same hotel room he used when he first arrived in the country, all of his belongings inside his original luggage.
He died of stomach cancer
at age 62 in Princeton, New Jersey.
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
; born in Chalandri
Chalandri
Chalandri or Halandri is a northern suburb in Athens, Greece, and a municipality of the Attica region...
, Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...
, Greece
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
on June 29, 1914, died on June 29, 1976, Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
), was a Greek
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
specializing in geometric topology
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
. He worked in isolation at Athens University being awarded a Ph.D on the recommendation of Carathéodory. In 1948 he was invited by Ralph Fox
Ralph Fox
Ralph Hartzler Fox was an American mathematician. As a professor at Princeton University, he taught and advised many of the contributors to the Golden Age of differential topology, and he played an important role in the modernization and main-streaming of knot theory.Ralph Fox attended Swarthmore...
to come as his guest at the Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
mathematics department. Fox had been impressed by a letter from Papakyriakopoulos which purported to prove Dehn's lemma
Dehn's lemma
In mathematics Dehn's lemmaasserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disc's interior, implies the existence of another piecewise-linear map of the disc which is an embedding and is identical to the original on the boundary of the...
. The proof, as it turned out was faulty, but Fox's sponsorship would continue for many years and enabled Papakyriakopoulos to work on his mathematics without concern of financial support.
Papakyriakopoulos is best known for his proofs of Dehn's lemma, the loop theorem
Loop theorem
In mathematics, in the topology of 3-manifolds, the loop theorem is a generalization of Dehn's lemma. The loop theorem was first proven by Christos Papakyriakopoulos in 1956, along with Dehn's lemma and the Sphere theorem....
, and the sphere theorem
Sphere theorem (3-manifolds)
In mathematics, in the topology of 3-manifolds, the sphere theorem of gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres.One example is the following:...
, three foundational results for the study of 3-manifold
3-manifold
In mathematics, a 3-manifold is a 3-dimensional manifold. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.Phenomena in three dimensions...
s. In honor of this work, he was awarded the first Veblen Prize in Geometry
Oswald Veblen Prize in Geometry
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen...
in 1964. From the early sixties
1960s
The 1960s was the decade that started on January 1, 1960, and ended on December 31, 1969. It was the seventh decade of the 20th century.The 1960s term also refers to an era more often called The Sixties, denoting the complex of inter-related cultural and political trends across the globe...
on, he mostly worked on the Poincaré conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
.
The following unusual limerick
Limerick (poetry)
A limerick is a kind of a witty, humorous, or nonsense poem, especially one in five-line or meter with a strict rhyme scheme , which is sometimes obscene with humorous intent. The form can be found in England as of the early years of the 18th century...
was composed by John Milnor
John Milnor
John Willard Milnor is an American mathematician known for his work in differential topology, K-theory and dynamical systems. He won the Fields Medal in 1962, the Wolf Prize in 1989, and the Abel Prize in 2011. Milnor is a distinguished professor at Stony Brook University...
, shortly after learning of several graduate students' frustration at completing a project where the work of every Princeton mathematics faculty member was to be summarized in a limerick:
-
-
-
- The perfidious lemma of Dehn
- Was every topologist's bane
- 'Til Christos Papa-
- kyriakopou-
- los proved it without any strain.
-
-
The phrase "without any strain" is not meant to indicate that Papa did not expend much energy in his efforts. Rather, it refers to Papa's "tower construction", which quite nicely circumvents much of the difficulty in the cut-and-paste efforts that preceded Papa's proof.
He sympathized with leftist politics. When he went to live in the USA, the Greek authorities reported him to the American authorities as a "communist".
He was a reclusive character, spending most of his time in his office listening to his beloved Wagner. Legend has it that in the US he lived for 25 years in the same hotel room he used when he first arrived in the country, all of his belongings inside his original luggage.
He died of stomach cancer
Stomach cancer
Gastric cancer, commonly referred to as stomach cancer, can develop in any part of the stomach and may spread throughout the stomach and to other organs; particularly the esophagus, lungs, lymph nodes, and the liver...
at age 62 in Princeton, New Jersey.