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One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers.
No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.
Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures.
Thus not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effective connection with each other.
The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.
If you help others, you will be helped, perhaps tomorrow, perhaps in one hundred years, but you will be helped. Nature must pay off the debt. It is a mathematical law and all life is mathematics.
Life has puffed and blown itself into a summer day, and clouds and spring billow over the heavens as if calendars were a listing of mathematical errors.
The essential fact is that all the pictures which science now draws of nature, and which alone seem capable of according with observational facts, are mathematical pictures.
It is utterly implausible that a mathematical formula should make the future known to us, and those who think it can would once have believed in witchcraft.
A display connected to a digital computer gives us a chance to gain familiarity with concepts not realizable in the physical world. It is a looking glass into a mathematical wonderland.
I am well aware of the disagreeable effect produced on the majority of humanity, by whatever relates, even at the slightest degree to calculations or mathematical reasonings.
I swam the race like I trained to swim it. It is not mathematical. I just let my body do it. It is a lot easier if you let your body do what it is trained for.
The mathematical phenomenon always develops out of simple arithmetic, so useful in everyday life, out of numbers, those weapons of the gods: the gods are there, behind the wall, at play with numbers.
If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.