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"The Science of Pure Mathematics in its modern development, may claim to be the most original creation of the human spirit."

"Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence."

"God made the integers, all the rest is the work of man."

"Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself."

"On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century."

"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."

"I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'."

"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere."

"The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful."

"For the things of this world cannot be made known without a knowledge of mathematics."

"All things began in Order, so shall they end, and so shall they begin again, according to the Ordainer of Order, and the mystical mathematicks of the City of Heaven."

"The numbers are a catalyst that can help turn raving madmen into polite humans."

"omnia apud me mathematica fiunt: With me everything turns into mathematics."

"Poetry is as exact a science as geometry."

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."

Mathematics is the science of what is clear by itself.

"The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience."

"A proof tells us where to concentrate our doubts."

"Number theorists are like lotus-eaters -- having once tasted of this food they can never give it up."

"Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar."

"...mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning."

"There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world."

"The knowledge of which geometry aims is the knowledge of the eternal."

"Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity."

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