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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.

Mathematicians who are only mathematicians have exact minds, provided all
things are explained to them by means of definitions and axioms; otherwise
they are inaccurate and insufferable, for they are only right when the
principles are quite clear.

And men of intuition who are only intuitive cannot have the patience to
reach to first principles of things speculative and conceptual, which they
have never seen in the world and which are altogether out of the common.

2. There are different kinds of right understanding; some have right
understanding in a certain order of