Authors:	Rowe, David E.
Title:	On the origins of Cantor’s paradox : what Hilbert left unsaid at the 1900 ICM in Paris
Online publication date:	24-Apr-2023
Year of first publication:	2023
Language:	english
Abstract:	The first two of the twenty-three unsolved problems that David Hilbert famously proposed at the 1900 International Congress of Mathematicians (ICM) in 1900 dealt with issues associated with the real number continuum. The first problem concerned Cantor’s continuum hypothesis, whereas the second dealt with Hilbert’s attempt to establish the existence of the continuum by proving the consistency of his axioms for characterizing its properties. Few have noted, however, that Hilbert himself linked the larger goals of Cantor’s theory of transfinite arithmetic with those of his own program for axiomatization. By carefully recounting Hilbert’s interactions with Cantor from 1897 onward, this paper shows how Hilbert’s understanding of “Cantor’s paradox” influenced the views he expressed at the 1900 ICM.
DDC:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-9000
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	The mathematical intelligencer Version of Record (VoR)
Publisher:	Springer
Publisher place:	Berlin u.a.
Issue date:	2023
ISSN:	1866-7414
Publisher DOI:	10.1007/s00283-022-10259-x
Appears in collections:	DFG-491381577-H