“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.”

— Georg Cantor

Grundlagen einer allgemeinen Mannigfaltigkeitslehre [Foundations of a General Theory of Aggregates] (1883)

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Georg Cantor 27

mathematician, inventor of set theory 1845–1918

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Context: My opinion concerning God differs widely from that which is ordinarily defended by modern Christians. For I hold that God is of all things the cause immanent, as the phrase is, not transient. I say that all things are in God and move in God, thus agreeing with Paul, and, perhaps, with all the ancient philosophers, though the phraseology may be different; I will even venture to affirm that I agree with all the ancient Hebrews, in so far as one may judge from their traditions, though these are in many ways corrupted. The supposition of some, that I endeavour to prove in the Tractatus Theologico-Politicus the unity of God and Nature (meaning by the latter a certain mass or corporeal matter), is wholly erroneous.
As regards miracles, I am of opinion that the revelation of God can only be established by the wisdom of the doctrine, not by miracles, or in other words by ignorance.

“When finding that people held the same views as I, I persuaded myself that I held them differently.”

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“This view [of the infinite], which I consider to be the sole correct one, is held by only a few.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

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Context: This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!

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“I shall here present the view that numbers, even whole numbers, are words, parts of speech, and that mathematics is their grammar.”

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Numbers were therefore invented by people in the same sense that language, both written and spoken, was invented. Grammar is also an invention. Words and numbers have no existence separate from the people who use them. Knowledge of mathematics is transmitted from one generation to another, and it changes in the same slow way that language changes. Continuity is provided by the process of oral or written transmission.
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“Geometry can in no way be viewed… as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I… realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.”

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“We naturally like what we have been accustomed to, and are attracted towards it. […] The same is the case with those opinions of man to which he has been accustomed from his youth; he likes them, defends them, and shuns the opposite views.”

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Source: The Guide for the Perplexed

“The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

As quoted in Mind Tools: The Five Levels of Mathematical Reality (1988) by Rudy Rucker. ~ ISBN 0395468108

“It is true that M. Fourier had the opinion that the principal end of mathematics was the public utility and the explanation of natural phenomena; but such a philosopher as he is should have known that the unique end of science is the honor of the human mind, and that from this point of view a question of number is as important as a question of the system of the world.”

Carl Gustav Jacob Jacobi (1804–1851) German mathematician

Letter to Legendre (July 2, 1830) in response to Fourier's report to the Paris Academy Science that mathematics should be applied to the natural sciences, as quoted in Science (March 10, 1911) Vol. 33 https://books.google.com/books?id=4LU7AQAAMAAJ&pg=PA359, p.359, with additional citations and dates from H. Pieper, "Carl Gustav Jacob Jacobi," Mathematics in Berlin (2012) p.46

“I look on myself as an instrument of the Almighty and go on my way regardless of transient opinions and views.”

Wilhelm II, German Emperor (1859–1941) German Emperor and King of Prussia

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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.”

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Georg Cantor 27

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