Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exist.
Number proceeds from unity.
I have often admired the mystical way of Pythagoras, and the secret magic of numbers.
Numbers are the free creation of the human mind.
Wherever there is number, there is beauty.
We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds.
[The] sole end of science is the honor of the human mind, and…under this title a question about numbers is worth as much as a question about the system of the world.
When you can measure what you are talking about and express it in numbers, you know something about it.
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit.
Thus number may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician.
Bridges would be safer if only people who knew the proper definition of a real number were allowed to design them.
The idea of the continuum seems simple to us. We have somehow lost sight of the difficulties it implies…We are told such a number as the square root of 2 worried Pythagoras and his school almost to exhaustion. Being used to such queer numbers from early childhood, we must be careful not to form a low idea of the mathematical intuition of these ancient sages; their worry was highly credible.
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.