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The essence of mathematics is not to make simple things complicated, but to make complicated things simple. |
The essence of mathematics is not to make simple things complicated, but to make complicated things simple. |
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds. |
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The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. |
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The piano's world encompasses glass-nerved virtuosi and stomping barrel-housers in fedoras; it is a world of pasture and storm, of perfumed smoke, of liquid mathematics. |
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence |
The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite. |
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There are things which seem incredible to most men who have not studied mathematics. |
There are things which seem incredible to most men who have not studied mathematics. |
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. |