Allegorical bits of history
in the "Hotel Infinity" story:
Set theory and the notions of cardinality were first developed by
Georg Cantor in the late 1800's.
Leopold Kronecker, another mathematician and a contemporary of
Cantor’s, felt that the only mathematical concepts
with validity were those whose construction could be described in a
step-by-step manner - using only a finite number of steps. He was
virulently opposed to Cantor’s notions of infinity, calling them
"meaningless." Kronecker tried to prevent the influential Crelle’s Journal from publishing Cantor’s work and for a time succeeded. If history is a judge, it has vindicated Cantor.
Cantor struggled with depression for much of his life, spent time
hospitalized, somewhat like the breakdown in the story, and died in a
sanatorium in 1918.
David Hilbert, perhaps one of the greatest
mathematicians in the early 20th
century, praising Cantor’s development
of set theory, proclaimed “No one will drive us [mathematicians] from
the paradise which Cantor
created for us.”
In a 1920’s lecture, Hilbert described a “Grand Hotel” with infinitely
many rooms; the
anecdote is remembered to this day as “Hilbert’s Hotel.” The anecdote
was far shorter than the story I've assigned, which was written in
1991.
Last Modified November 25, 2009.
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