On Georg Cantor

"Thus far, gentlemen, I have been insisting very strenuously upon what the most vulgar common sense has every disposition to assent to and only ingenious philosophers have been able to deceive themselves about. But now I come to a category which only a more refined form of common sense is prepared willingly to allow, the category which of the three is the chief burden of Hegel's song, a category toward which the studies of the new logico-mathematicians, Georg Cantor and the like, are steadily pointing, but to which no modern writer of any stripe, unless it be some obscure student like myself, has ever done anything approaching to justice." (Charles S Peirce, "Pragmatism and Pragmaticism", 1903)

"It is true that the field of mathematical activity proper, both in analysis and in geometry, is not directly affected by the antinomies. They appear chiefly in a region of extreme generalization, beyond the domain in which the concepts of these disciplines are actually used. It is in general not difficult to take precautionary measures in order to avoid the dangerous region. This is the main reason why many mathematicians recoiled so quickly from the initial shock caused by the appearance of the antinomies. The very fact that one continued to speak of paradoxes, or antinomies, rather than of contradictions serves as an indication that deep in their heart most modern mathematicians did not want to be expelled from the paradise into which Cantor’s discoveries had led them." (Abraham Fraenkel et al, "Foundations of Set Theory" 2nd Ed., 1953)

"The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul's quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)

"Formally, a Cantor set is defined as a set that is totally disconnected, closed, and perfect. A totally disconnected set is a set that contains no intervals and therefore has no interior points. A closed set is one that contains all its boundary elements. (A boundary element is an element that contains elements both inside and outside the set in arbitrarily small neighborhoods.) A perfect set is a nonempty set that is equal to the set of its accumulation points. All three conditions are met by our middle-third - erasing construction, the original Cantor set." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990

"Why was Cantor so vehemently opposed to infinitesimals? In his valuable essay, 'The Metaphysics of the Calculus', Abraham Robinson suggests that Cantor already had enough problems trying to defend transfinite numbers. It seems likely that, consciously or otherwise, Cantor deemed it politically wise to go along with orthodox mathematicians on the question of infinitesimals. Cantor's stance might be compared to that of a pro-marijuana Congressional candidate who advocates harsh penalties for the sale or use of heroin." (Rudy Rucker, "Infinity and the Mind", 2005)

"Georg Cantor claimed the essence of mathematics lies in its freedom. But mathematicians do not pick problems from thin air for the pleasure of solving them. To the contrary, a mark of greatness resides in the ability to identify the most interesting problems in the framework of what is already known." (Benoît B Mandelbrot, "The Fractalist", 2012)

"No one shall expel us from the paradise which Cantor has created for us." (David Hilbert)