''Cantor's paradise'' is an expression used by in describing

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

and infinite

cardinal number In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the cas ...

s developed by

Georg Cantor Georg Ferdinand Ludwig Philipp Cantor ( ; ; – 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a foundations of mathematics, fundamental theory in mathematics. Cantor establi ...

. 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

* * * 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. *"About Cantor's Paradise". Medium. A Medium Corporation. Retrieved 24 January 2021. Set theory David Hilbert {{Settheory-stub