##### Sun Tze (5th - 6th century)

The control of large numbers is possible, and like unto that of small numbers, if we subdivide them.

##### Swift, Jonathan

If they would, for Example, praise the Beauty of a Woman, or any other Animal, they describe it by Rhombs, Circles, Parallelograms, Ellipses, and other geometrical terms ...

"A Voyage to Laputa" in Gulliver's Travels.

##### Sylvester, J. J. (1814 - 1897)

[T]here is no study
in the world which
brings into more
harmonious action
all the faculties of
the mind than
[mathematics], ...
or, like this, seems
to raise them, by
successive steps of
initiation, to
higher and higher
states of conscious
intellectual being.

Presidential Address
to British
Association, 1869.

##### Sylvester, J.J. (1814 - 1897)

So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting what he is learning, of propagating through others the ideas and impressions seething in his own brain, without stunting and atrophying his moral nature and drying up the surest sources of his future intellectual replenishment.

##### Sylvester, J.J. (1814 - 1897)

[On graph
theory:]

The
theory of
ramification is one
of pure colligation,
for it takes no
account of magnitude
or position;
geometrical lines
are used, but these
have no more real
bearing on the
matter than those
employed in
genealogical tables
have in explaining
the laws of
procreation.

In H. Eves,
Mathematical Circles
Adieu, Boston:
Prindle, Weber and
Schmidt, 1977.

##### Sylvester, J.J. (1814 - 1897)

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.

Presidential Address to British Association, 1869.

##### Sylvester, J.J. (1814 - 1897)

The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance.

Presidential Address to British Association, 1869.

##### Sylvester, J.J. (1814 - 1897)

I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty ... as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize.

##### Sofya Kovalevskaya

Many people who have
never had occasion
to learn what
mathematics is
confuse it with
arithmetic and
consider it a dry
and arid science.
In actual fact it is
the science which
demands the utmost
imagination. One of
the foremost
mathematicians of
our century says
very justly that it
is impossible to be
a mathematician
without also being a
poet in spirit. . .
. It seems to me
that the poet must
see what others do
not see, must see
more deeply than
other people. And
the mathematician
must do the same.

##### Stanislaw Ulam

Knowing what is big
and what is small is
more important than
being able to solve
partial differential
equations.

MacTutor History of
Mathematics Archive