The Seventh Meeting of the
ORESME Reading Group
September 14-15, 2001
Northern Kentucky University
In attendance:
Chris Christensen, Northern Kentucky University
Dan Curtin, Northern Kentucky University, host
Richard Davitt, Universty of Louisville
Hans Fischer, Xavier University
Kevin Kirby, Northern Kentucky University
Chuck Holmes, Miami University
David Kullman, Miami University
Danny Otero, Xavier University
Dick Pulskamp, Xavier University
We met for dinner Friday evening at Lyon's Grille, a small, out-of-the-way,
but classy restaurant in booming downtown Ft. Thomas.
We convened after the meal at the NKU Applied Science Building to
read the
following papers by Georg Cantor:
[1] Über eine Eigenschaft des Inbegriffs aller reellen algebraischen
Zahlen.
Journal f. reine und angew. Math. 77 (1874), 258-262. = Gesammelte
Abhandlungen,
115-118. English translation entitled "On a property of the set
of real
algebraic numbers," in volume 2, pp. 839-843 of From Kant
to Hilbert.
A Source Book in the Foundations of Mathematics edited by William
Ewald,
Oxford: Clarendon Press, 1999.
[2] Über eine elementare Frage der Mannigfaltigkeitslehre.
Jahresber. der
Dt. Math.-Verein. 1 (1890/91), 75-78. = Gesammelte Abhandlungen,
278-280.
English translation entitled "On an elementary question in the
theory of
manifolds," in volume 2, pp. 923-940 of From Kant to Hilbert.
A Source Book
in the Foundations of Mathematics edited by William Ewald, Oxford:
Clarendon
Press, 1999.
[3] A letter of June 18, 1886 from Cantor to F. Goldscheider, a
Berlin
Gymnasium teacher and admirer of Cantor's work. Found in
Meschkowski, Herbert, Ways of Thought of Great Mathematicians,
San Francisco:
Holden-Day, 1964, 95-103.
[4] Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Ein mathematisch-
philosophischer Versuch in der Lehre des Unendlichen. Leipzig:
1883. B.G. Teubner.
= Gesammelte Abhandlungen, 165-208. English translation entitled
"Foundations
of a General Theory of Manifolds: a Mathematico-Philosophical Investigation
into the Theory of the Infinite," in volume 2, pp. 878-920
of From Kant to
Hilbert. A Source Book in the Foundations of Mathematics
edited by William Ewald,
Oxford: Clarendon Press, 1999.
We began however with a viewing of Joseph Dauben's lecture, "Georg
Cantor: The
Battle for Transfinite Set Theory" (AMS, 1989, 60 minutes, ISBN
0-8218-8015-2),
delivered at the 1988 Joint Meeting and AMS Centennial in Atlanta.
Richard Davitt
was kind enough to bring a copy from U of Louisville (which he
was forced to leave
behind when the VCR refused to give it back!). This provided
us with a good
deal of introductory biographical information on Cantor and set
the stage for
our discussions. Copies of Dauben's biography of Cantor
[Dauben, Joseph W., Georg Cantor. His Mathematics and the Philosophy
of the
Infinite, Cambridge MA: Harvard University Press, 1979. Reprinted
by Princeton
University Press, 1990.]
were available and found to be quite useful. The following
issues saw a good deal
of discussion:
Cantor's definition of real number in the "Grundlagen";
the interesting connection between Cantor's
discussion of iterated derived
sets (P, P', P'', P''',
... ) and the study of transfinite numbers.
The discussion continued Saturday morning over bagels and bananas.
We finished
with talk about future meetings. We still hope to meet in
Louisville in the
spring with Della Fenster to read a paper of L.E. Dickson.
Another suggestion
was to read Julius Petersen's 1891 "Die theorie der regulären
graphs" (Acta Math.
XV 193-220), the first comprehensive publication in modern graph
theory.
Respectfully submitted,
Danny Otero