Alfred North Whitehead
There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.
The study of mathematics is apt to commence in disappointment…we are told that by its aid the stars are weighed and the billion of molecules in a drop of water are counted. Yet, like the ghost of Hamlet’s father, this great science eludes the efforts of our mental weapons to grasp it.
Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings.
…zero…is only forced on us by the needs of cultivated thought.
I regret that it has been necessary for me in this lecture to administer such a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are.
The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit.
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
We think of the number “five” as applying to appropriate groups of any entities whatsoever—to five fishes, five children, five apples, five days…We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the members of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it.