of his defeat lies in the supposition that the
Minister is a fool, because he has acquired renown as a poet. All fools
are poets; this the Prefect feels; and he is merely guilty of a _non
distributio medii_ in thence inferring that all poets are fools."

"But is this really the poet?" I asked. "There are two brothers, I know;
and both have attained reputation in letters. The Minister, I believe,
has written learnedly on the Differential Calculus. He is a
mathematician and no poet."

"You are mistaken; I know him well; he is both. As poet and
mathematician, he would reason well; as mere mathematician, he could not
have reasoned at all, and thus would have been at the mercy of the
Prefect."

"You surprise me," I said, "by these opinions, which have been
contradicted by the voice of the world. You do not mean to set at naught
the well-digested idea of centuries? The mathematical reason has long
been regarded as the reason _par excellence_."

"'Il y a a parier,'" replied Dupin, quoting from Chamfort, "'que toute
idee publique, toute convention recue, est une sottise, car elle a
convenue au plus grand nombre.' The mathematicians, I grant you, have
done their best to promulgate the popular error to which you allude, and
which is none the less an error for its promulgation as truth. With an
art worthy a better cause, for example, they have insinuated the term
'analysis' into application to algebra. The French are the originators
of this particular deception; but if a term is of any importance, if
words derive any value from applicability, then 'analysis' conveys
'algebra' about as much as, in Latin, '_ambitus_' implies 'ambition,'
'_religio_' 'religion,' or '_homines honesti_' a set of honourable men."

"You have a quarrel on hand, I see," said I, "with some of the
algebraists of Paris; but proceed."

"I dispute the availability, and thus the value of that reason which is
cultivated in any especial form other than the abstractly logical. I
dispute, in particular, the reason educed by mathematical study. The
mathematics are the science of form and quantity; mathematical reasoning
is merely logic applied to observation upon form and quantity. The great
error lies in supposing that even the truths of what is called pure
algebra are abstract or general truths. And this error is so egregious
that I am confounded at the universality with which it has been
received. Mathematical axioms are not axioms of general truth. What is