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I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise.
--
Alexander Stepanov, in "Bjarne Stroustrup: Evolving a language in and for the real world: C++ 1991-2006" in ACM HOPL-III (June 2007)

 

Georg Cantor

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I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes.

 

Alexander Stepanov

 

Throughout the long battle for the acceptance of his views, Darwin was plagued continually by his inability to compress the scale of nature to demonstrate a transformation of species to his critics. Had he known it, an example was at hand which would have provided him with the proof he needed. The case was an exceedingly rare one, in which a major evolutionary change occurred in the brief interval of fifty years. The animal which underwent the transformation was a member of the insect world, the humble Peppered Moth, found in abundance throughout England.

 

Charles Darwin

 

Glorious transformation! glorious translation! I seem already to behold the wondrous scene. The sea and the land have given up their dead! the quickened myriads have been judged according to their works. And now, an innumerable company, out of all nations and tribes and tongues, ascend with the Mediator towards the kingdom of His Father. Can it be that these, who were born children of earth, who were long enemies to God by wicked works, are to enter the bright scenes of paradise? Yes, He who leads them has washed them in His blood; He who leads them has sanctified them by His Spirit.

 

Henry Melvill

 

While [Plato] affirmed with emphasis that the place of the individual in society should not be determined by birth or wealth or any conventional status, but by his own nature as discovered in the process of education, he had no perception of the uniqueness of individuals. For him they fall by nature into classes, and into a very small number of classes at that.

 

John Dewey

 

“Why, if I may ask, are you called the Blue Knight?”
“I am thought to be melancholy.”
“On what evidence?”
“Just my temperament, I suppose. I’ve always been rather melancholy, even as a child. Spent a lot of time plucking at the counterpane, as it were. It grew worse as I grew older. Also, I published a book. It was called On the Impossibility of Paradise.”
“What was the argument?”
“I argued that the idea of a former paradise, which had been lost and might be regained either in this world or in the next, did not square with my experience.”
“Personal experience.”
“Yes. I wasn’t happy even in the womb. The womb, for me, was far from a paradise. I remember distinctly. My mother was a very modern person—advanced, don’t you know. Fond of Alban Berg, the Wozzeck man. Not only was I forced repeatedly to listen to Wozzeck, in the womb, but also to Lulu, which is even worse, from the fetal point of view. These horrors aside, there was the poetry of Wyndham Lewis, proprietor of Blast. Blast was the name of his magazine. Can you imagine calling your magazine Blast? Going to crack consciousness wide open, he was. These tidderly-push artists and their conceits—the poetry was of a piece. I had to listen to it. In the womb. In addition, there were certain odd substances entering the bloodstream—do you know what Kif is?”
“No idea.”
“Better thus. In sum, my womb time was quite hellish, and upon being expelled I found the larger arena not much of an improvement. I don’t mean to complain, of course,I’m just trying to suggest—”
“No, no,” said Sir Roger. “Say on. Isupposen we should be doing search-and-destroy, but your remarks are of the greatest interest to me.”
“Good of you,” said the Blue Knight. “The basic contradiction I located or felt I had located was in terms of dramatic values. Paradise, the Fall, and the return to Paradise—it’s not a story. It’s too symmetrical. There are no twists. Just Paradise, zip, Fall, zip, and Paradise again, zip. And I had a very strong feeling, an intuition if you will, that even if Paradise were regained it would have music by Milhaud and frescoes by the Italian Futurists.”

 

Donald Barthelme