Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
It was an All-in-One and One-in-All of limitless being and self — not merely a thing of one Space-Time continuum, but allied to the ultimate animating essence of existence’s whole unbounded sweep — the last, utter sweep which has no confines and which outreaches fancy and mathematics alike. It was perhaps that which certain secret cults of earth have whispered of as YOG-SOTHOTH, and which has been a deity under other names; that which the crustaceans of Yuggoth worship as the Beyond-One, and which the vaporous brains of the spiral nebulae know by an untranslatable Sign.
Pure mathematics is, in its way, the poetry of logical ideas.[Die reine Mathematik ist auf ihre Art die Poesie logischer Gedanken.]
Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable.
Mechanics are the Paradise of mathematical sciences, because here we come to the fruits of mathematics.
It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza’s God, it won’t love us in return.