From: "Charles H. Giffen"
Subject: Re: Theorems/Lemmas
Date: Wed, 03 Mar 1999 11:01:43 -0500
Newsgroups: sci.math
To: "Peter L. Montgomery"
Keywords: Papakyriakopolous' Theorems (historical)
Peter L. Montgomery wrote:
>
[snip]
> History may give something a different rating than its author did.
> Examples are Zorn's Lemma (set theory) and Fatou's Lemma (measure theory).
> Fermat's Last Theorem should have been called Fermat's Last Conjecture
> (since it lacked a proof) until rcently.
> --
> Peter-Lawrence.Montgomery@cwi.nl Home: San Rafael, California
> Microsoft Research and CWI
And of course Dehn's Lemma was one of the most important theorems
of the topology of 3-manifolds -- but Dehn's proof of his Lemma
had a major gap (pointed out, I believe by Kneser in the 20's),
and the result (still known as Dehn's Lemma) was finally proved
by Christos D. Papakyriakapoulos in about 1956/57. At about the
same time, Papa proved the famed Loop Theorem and the Sphere Theorem --
but none of these three theorems ever became became
known as the Theorem of Papakyriakapoulos (or Papa's Theorem),
for Papa took the careful precaution of always referring to his
theorems as Dehn's Lemma, the Loop Theorem, and the Sphere Theorem,
so that by calling them such in his own papers, none of them would
(hopefully) ever be referred to as Papa's Theorem.
Why? -- because Papa was entirely too modest and even told me and
some others that theorems should not be named for people (and he
only deferred to calling his theorm Dehn's Lemma because of the
historical precedent) -- essentially expressing the viewpoint that
mathematicians should not be so egocentric. He also was careful
top point out that Dehn's Lemma was not called as such by Dehn
himself. And he smiled his famous grin and burst out laughing
when it was pointed out to him that it might cost a lot of printer's
ink if any of his theorems were ever commonly referred to as
Papakyriakapoulos' Theorem.
--Chuck Giffen