Papakyriakopoulos worked in isolation at Athens Polytechnic as research assistant to Professor Nikolaos Kritikos. But he was enrolled as research student at Athens University, being awarded a PhD in 1943 on the recommendation of Constantin Carathéodory. In 1948, he was invited by Ralph Fox to come as his guest at the Princeton University mathematics department because Fox had been impressed by a letter from Papakyriakopoulos that 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 for 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-manifolds. In honor of this work, he was awarded the first Oswald Veblen Prize in Geometry in 1964. From the early 1960s on, he mostly worked on the Poincaré conjecture. Bernard Maskit produced counterexamples about his proof three times.
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 perfidious lemma of Dehn
- Was every topologist's bane
- 'Til Christos D. Pap-
- 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.
Papakyriakopoulos sympathized with leftist politics 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. 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.
- Papakyriakopoulos, Christos (1963). "A reduction on the Poincaré conjecture to other conjectures. II" (PDF). Bulletin of the American Mathematical Society. 69 (3): 399–401. doi:10.1090/S0002-9904-1963-10944-1. MR 0149455.
- John Willard Milnor, John McCleary, Homotopy, Homology, and Manifolds, American Mathematical Society, 2009, p. 354.
- Article in Popular Science by Apostolos Doxiadis
- E Spandagou: Christos Papakyriakopoulos the hermit of Princeton (Greek), Athens 2008 (Aithra)
- NTUA's page Archived 2012-03-25 at the Wayback Machine on Papakyriakopoulos incorrectly lists his place of death as New York.
- Papakyriakopoulos, C. D. (1946). "Ein neuer Beweis fur die Invariance der Homologiegruppe eines Komplexes (Greek)". Bull. Soc. Math. Greece. Athens, Greece: Greek Mathematical Society. 22: 1–154.
- Papakyriakopoulos, C. D. (1957). "On Dehn's Lemma and the Asphericity of Knots". Proceedings of the National Academy of Sciences of the United States of America. 43 (1): 169–172. Bibcode:1957PNAS...43..169P. doi:10.1073/pnas.43.1.169. PMC 528404. PMID 16589993.
- Papakyriakopoulos, C. D. (1957). "On Dehn's Lemma and the Asphericity of Knots". Annals of Mathematics. 66 (1): 1–26. doi:10.2307/1970113. JSTOR 1970113.