Quotations by Georg Cantor


In mathematics the art of proposing a question must be held of higher value than solving it.
(A thesis defended at Cantor's doctoral examination)

The essence of mathematics lies in its freedom.
Quoted in D MacHale, Comic Sections (Dublin 1993)

Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.

Je le vois, mais je ne le crois pas!
I see it but I don't believe it!
Letter to R Dedekind regarding results of Theory of Manifolds (1877)

My theory stands as firm as a rock; every arrow directed against it will quickly return to the archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.

A set is a Many that allows itself to be thought of as a One.

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

In mathematics the art of proposing a question must be held of higher value than solving it.

The essence of mathematics lies in its freedom.


JOC/EFR April 2011

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