"The truth is that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space."

“There is no science which teaches the harmonies of nature more clearly than mathematics.”

“Pythagoras says that number is the origin of all things, and certainly the law of number is the key that unlocks the secrets of the universe. But the law of number possesses an immanent order, which is at first sight mystifying, but on a more intimate acquaintance we easily understand it to be intrinsically necessary; and this law of number explains the wondrous consistency of the laws of nature.”

“Some imagine that science is limited to the lower sorts of natural facts only. Religious and moral facts have been too little heeded by our scientists. Thus people came to think that science and religion move in two different spheres. That is not so. The facts of our soul-life must be investigated and stated with scientific accuracy, and our clergy should be taught to purify religion with the criticism of scientific methods. They need not fear for their religious ideals. So far as they are true, and their moral kernel is true, they will not suffer in the crucible of science. Religion will not lose one iota of its grandeur, if it is based upon a scientific foundation; all that it will lose is the errors that are connected with religion and the sooner they are lost the better for us.”

“There is no prophet which preaches the superpersonal God more plainly than mathematics.”

“When Luther stood before the emperor and the representatives of church and state, he begged to be refuted, and if he were refuted, he promised to keep silence; but as he was not, he continued to preach and he preached boldly in the name of truth as one that had authority. Therefore let religious progress be made as in the era of the Reformation, not in complaisance to popular opinion, but squarely in the name of truth.”

“Infinity is the land of mathematical hocus pocus. There Zero the magician is king. When Zero divides any number he changes it without regard to its magnitude into the infinitely small , and inversely, when divided by any number he begets the infinitely great . In this domain the circumference of the circle becomes a straight line, and then the circle can be squared. Here all ranks are abolished, for Zero reduces everything to the same level one way or another. Happy is the kingdom where Zero rules!”