Cantor's paradise

Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können. (From the paradise, that Cantor created for us, no-one can expel us.)

Hilbert (1926, p. 170), a lecture given in Münster to Mathematical Society of Westphalia on 4 June 1925

Cantor's paradise is an expression used by David Hilbert (1926, page 170) in describing set theory and infinite cardinal numbers developed by Georg Cantor. The context of Hilbert's comment was his opposition to what he saw as L. E. J. Brouwer's reductive attempts to circumscribe what kind of mathematics is acceptable; see Brouwer–Hilbert controversy.

References

• Ferreirós, José (2008). Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics (2nd revised ed.). Basel: Birkhäuser. ISBN 3-7643-8350-X. Zbl 1119.03044.
• Hilbert, David (1926), "Über das Unendliche", Mathematische Annalen, 95 (1): 161–190, doi:10.1007/BF01206605, JFM 51.0044.02
• Saharon Shelah. You can enter Cantor's paradise! Paul Erdős and his mathematics, II (Budapest, 1999), 555–564, Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Budapest, 2002.
• Peckhaus, Volker. Fixing Cantor's paradise: the prehistory of Ernst Zermelo's axiomatization of set theory. New approaches to classes and concepts, 11–22, Stud. Log. (Lond.), 14, Coll. Publ., London, 2008.