An introduction to mathematics (1911) by Alfred North Whitehead
"A show of violence," if ever excusable, may surely be "offered" to the trivial results which occupy the pages of some elementary mathematical treatises.
The reason for this failure of the science to live up to its reputation is that its fundamental ideas are not explained to the student disentangled from the technical procedure which has been invented to facilitate their exact presentation in particular instances. Accordingly, the unfortunate learner finds himself struggling to acquire a knowledge of a mass of details that are not illuminated by any general conception.
Without a doubt, the technical facility is a first requisite for valuable mental activity: we shall fail to appreciate the rhythm of Milton or the passion of Shelley, so long as we find it necessary to spell the words and are not quite certain of the forms of the individual letters. In this sense, there is no royal road to learn ing. But it is equally an error to confine attention to technical processes, excluding consideration of general ideas. Here lies the road to pedantry.
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