Christos Dimitriou Papakyriakopoulos (), commonly known as Papa (
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
: Χρήστος Δημητρίου Παπακυριακόπουλος ; June 29, 1914 – June 29, 1976), was a
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
specializing in
geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
History
Geometric topology as an area distinct from algebraic topology may be said to have originated i ...
.
Early life
Papakyriakopoulos was born in
Chalandri
Chalandri ( el, Χαλάνδρι, Ancient Greek: Φλύα, ''Phlya'') is a suburb in the northern part of the Athens agglomeration, Greece. It is a municipality of the Attica region.
Geography
Chalandri is a suburb in Northern Athens, around fr ...
, then in the
Municipality of Athens
Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates a ...
, now in
North Athens
North is one of the four compass points or cardinal directions. It is the opposite of south and is perpendicular to east and west. ''North'' is a noun, adjective, or adverb indicating direction or geography.
Etymology
The word ''north'' is ...
.
Career
Papakyriakopoulos worked in isolation at Athens Polytechnic as research assistant to Professor Nikolaos Kritikos. But he was enrolled as research student at
Athens University
The National and Kapodistrian University of Athens (NKUA; el, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών, ''Ethnikó ke Kapodistriakó Panepistímio Athinón''), usually referred to simply as the Univers ...
, being awarded a
PhD in 1943 on the recommendation of
Constantin Carathéodory
Constantin Carathéodory ( el, Κωνσταντίνος Καραθεοδωρή, Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant ...
. In 1948, he was invited by
Ralph Fox
Ralph Hartzler Fox (March 24, 1913 – December 23, 1973) 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 ...
to come as his guest at the
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
mathematics department because Fox had been impressed by a letter from Papakyriakopoulos that purported to prove
Dehn's lemma In mathematics, Dehn's lemma asserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear map of the disk which is an embedding and is ...
. 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 for financial support.
Papakyriakopoulos is best known for his proofs of
Dehn's lemma In mathematics, Dehn's lemma asserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear map of the disk which is an embedding and is ...
, the
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.
A simple and useful ve ...
, and the
sphere theorem
In Riemannian geometry, the sphere theorem, also known as the quarter-pinched sphere theorem, strongly restricts the topology of manifolds admitting metrics with a particular curvature bound. The precise statement of the theorem is as follows. ...
, three foundational results for the study of
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds lo ...
s. In honor of this work, he was awarded the first
Oswald Veblen Prize in Geometry
__NOTOC__
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. The Veblen Prize is now worth US$5000, and is ...
in 1964. From the early 1960s on, he mostly worked on the
Poincaré conjecture
In the mathematics, mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the Characterization (mathematics), characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dim ...
.
Bernard Maskit
Bernard Maskit is an American mathematician known for his expertise in Kleinian groups. The Maskit slice through the moduli space of Kleinian groups is named after him; he is the author of the book ''Kleinian Groups'' (Grundlehren der Mathematisc ...
produced counterexamples about his proof three times.
Tribute
The following unusual
limerick
Limerick ( ; ga, Luimneach ) is a western city in Ireland situated within County Limerick. It is in the province of Munster and is located in the Mid-West which comprises part of the Southern Region. With a population of 94,192 at the 2016 ...
was composed by
John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Uni ...
, 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 D. Pap-
:::: akyriakop-
::::oulos proved it without any strain.
This may be the only limerick where one word spans three lines. 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.
Other activities
Papakyriakopoulos sympathized with leftist politics
[Article in ''Popular Science'' by Apostolos Doxiadis](_blank)
/ref> and in 1941 joined the student branch of the National Liberation Front (EAM). When he went to live in the US, in 1948 the Greek authorities reported him to the American authorities as a "dangerous communist" and asked for his extradition, but Princeton Institute of Advanced Study gave him protection as it had done with others suffering political persecution.
He was a reclusive character, spending most of his time in his office listening to his beloved Richard Wagner
Wilhelm Richard Wagner ( ; ; 22 May 181313 February 1883) was a German composer, theatre director, polemicist, and conductor who is chiefly known for his operas (or, as some of his mature works were later known, "music dramas"). Unlike most op ...
. Legend has it that in the United States 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.
Death
Papakyriakopoulos died of stomach cancer
Stomach cancer, also known as gastric cancer, is a cancer that develops from the lining of the stomach. Most cases of stomach cancers are gastric carcinomas, which can be divided into a number of subtypes, including gastric adenocarcinomas. Lymph ...
at age 62 in Princeton, New Jersey
Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
.NTUA's page
on Papakyriakopoulos incorrectly lists his place of death as New York
New York most commonly refers to:
* New York City, the most populous city in the United States, located in the state of New York
* New York (state), a state in the northeastern United States
New York may also refer to:
Film and television
* '' ...
.
See also
*
List of Greek mathematicians
In historical times, Greek civilization has played one of the major roles in the history and development of Greek mathematics. To this day, a number of Greek mathematicians are considered for their innovations and influence on mathematics.
Anci ...
Notes
References
*
*
*
External links
*
*
*
{{DEFAULTSORT:Papakyriakopoulos, Christos
1914 births
1976 deaths
20th-century Greek mathematicians
Topologists
Princeton University faculty
Deaths from stomach cancer
Deaths from cancer in New Jersey
National and Kapodistrian University of Athens alumni
Scientists from Athens