Georg Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantorwas a German mathematician. He invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work...
NationalityGerman
ProfessionMathematician
Date of Birth3 March 1845
CountryGermany
The essence of mathematics lies in its freedom.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
The essence of mathematics lies precisely in its freedom.
Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
In mathematics the art of proposing a question must be held of higher value than solving it.
A set is a Many that allows itself to be thought of as a One.
To ask the right question is harder than to answer it.
In mathematics the art of asking questions is more valuable than solving problems.
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.
One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.
started to tell his friends that he had not been the inventor of the ideas about infinity that he had published. He was merely a mouthpiece, inspired by God to communicate parts of the mind of God to everyone else.
Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!
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I realize 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.