In every department of physical science there is only so much science, properly so-called, as there is mathematics.
The instruction of children should aim gradually to combine knowing and doing. Among all sciences mathematics seems to be the only one of a kind to satisfy this aim most completely.
The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience
I assert that, in any particular natural science, one encounters genuine scientific substance only to the extent that mathematics is present.
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