The longer mathematics lives the more abstract—and therefore, possibly also the more practical—it becomes.
TOPICS: abstraction, practicality
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.
TOPICS: numbers, abstraction