In every department of physical science there is only so much science, properly so-called, as there is mathematics.
The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience
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.
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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