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Quote by Georg Cantor

“My theory stands as firm as a rock; every arrow directed against it will return quickly to its 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.”

Quote by Georg Cantor

Author

German mathematician and founder of set theory, a pioneer in the theory of infinity. His research on the foundations and logical structure of mathematics has had a profound impact on modern mathematics. more

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“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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Author:Georg Cantor

“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.”

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Author:Georg Cantor

“No human investigation can claim to be scientific if it doesn't pass the test of mathematical proof.”

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Author:Leonardo da Vinci

“My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.”

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Book:A Budget of Paradoxes Reprinted, with the Author's Additions, from the Athenaeum Augustus De Morgan

Source: A Budget of Paradoxes Reprinted, with the Author's Additions, from the Athenaeum Augustus De Morgan

“Although my knowledge grows more and more, nevertheless I do not for that reason believe that it can ever be actually infinite, since it can never reach a point so high that it will be unable to attain any greater increase.”

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Book:Discourse on Method and Meditations

Source: Discourse on Method and Meditations

“Neither the true nor the false roots are always real; sometimes they are imaginary; that is, while we can always imagine as many roots for each equation as I have assigned, yet there is not always a definite quantity corresponding to each root we have imagined.”

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Author:Rene Descartes

“We call infinite that thing whose limits we have not perceived, and so by that word we do not signify what we understand about a thing, but rather what we do not understand.”

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“Calculus works by making visible the infinitesimally small.”

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Book:Sets, Functions, and Logic: An Introduction to Abstract Mathematics, Third Edition

Source: Sets, Functions, and Logic: An Introduction to Abstract Mathematics, Third Edition

“The increased abstraction in mathematics that took place during the early part of this century was paralleled by a similar trend in the arts. In both cases, the increased level of abstraction demands greater effort on the part of anyone who wants to understand the work.”

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Author:Keith Devlin

“Since I found that one could make a case shadow from a three-dimensional thing, any object whatsoever - just as the projecting of the sun on the earth makes two dimensions - I thought that by simple intellectual analogy, the fourth dimension could project an object of three dimensions, or, to put it another way, any three-dimensional object, which we see dispassionately, is a projection of something four-dimensional, something we are not familiar with.”