🚀 go-pugleaf

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
mathematicians are intuitive and that men of intuition are mathematicians,
because mathematicians wish to treat matters of intuition mathematically and
make themselves ridiculous, wishing to begin with definitions and then with
axioms, which is not the way to proceed in this kind of reasoning. Not that
the mind does not do so, but it does it tacitly, naturally, and without
technical rules; for the expression of it is beyond all men, and only a few
can feel it.

Intuitive minds, on the contrary, being thus accustomed to judge at a single
glance, are so astonished when they are presented with propositions of which
they understand nothing, and the way to which is through definitions and
axioms so sterile, and which they are not accustomed to see thus in detail,
that they are repelled and disheartened.

But dull minds are never either intuitive or mathematical.

Mathematicia