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minds
would be mathematical if they could turn their eyes to the principles of
mathematics to which they are unused.
The reason, therefore, that some intuitive minds are not mathematical is
that they cannot at all turn their attention to the principles of
mathematics. But the reason that mathematicians are not intuitive is that
they do not see what is before them, and that, accustomed to the exact and
plain principles of mathematics, and not reasoning till they have well
inspected and arranged their principles, they are lost in matters of
intuition where the principles do not allow of such arrangement. They are
scarcely seen; they are felt rather than seen; there is the greatest
difficulty in making them felt by those who do not of themselves perceive
them. These principles are so fine and so numerous that a very delicate and
very clear sense is needed to perceive them, and to judge rightly and justly
when they are perceived, without for the most part being able to demonstrate
them in order as in mathematics, because the principles are not known to us
in the same way, and because it would be an endless matter to undertake it.
We must see the matter at once, at one glance, and not by a process of
reasoning, at least to a certain degree. And thus it is rare that
mat
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