If all art aspires to the condition of music,
all the sciences aspire to the condition of mathematics.
***
It is a pleasant surprise to [the mathematician]
and an added problem
if he finds that the arts can use his calculations,
or that the senses can verify them,
much as if a composer found that sailors
could heave better when singing his songs.
The idea of the continuum seems simple to us.
We have somehow lost sight of the difficulties it implies ...
We are told such a number as the square root of 2
worried Pythagoras and his school almost to exhaustion.
Being used to such queer numbers from early childhood,
we must be careful not to form a low idea
of the mathematical intuition of these ancient sages;
Mathematical rigor is like clothing;
in its style
it ought to suit the occasion,
and
it diminishes comfort
and
restrains freedom of movement
if it is either
too lose
or
too tight.
Arithmetic is one of the oldest branches, perhaps the very oldest branch, of human knowledge; and yet some of its most abstruse secrets lie close to its tritest truths.
***
Poor teaching leads to the inevitable idea that the subject (mathematics) is only adapted to peculiar minds, when it is the one universal science and the one whose ... ground rules are taught us almost in infancy and reappear in the motions of the universe.
Albert Einstein
Profession: physicist.
Born 1879, Ulm, Germany. Died 1955,
Princeton, New Jersey.
The creative principle resides in mathematics.
In a certain sense, therefore, I hold it true that
pure thought
can grasp reality,
as the ancients dreamed.
From the time of Kepler to that of Newton,
and from Newton to Hartley,
not only all things in external nature,
but the subtlest mysteries of life and organization,
and even of the intellect
and moral being,
were conjured within the circle of mathematical formulae.
The scientist does not study nature because it is useful;
he studies it because he delights in it,
and he delights in it because it is beautiful.
If nature were not beautiful, it would not be worth knowing,
and if nature were not worth knowing,
life would not be worth living.
The mathematician’s best work is art,
a high perfect art,
as daring as the most secret dreams of imagination,
clear and limpid.
Mathematical genius
and
artistic genius
touch one another.
Profession: mathematician, author.
Born 1908, Brooklyn, New York.
Died 1992, Brooklyn, New York.
"The tantalizing and compelling pursuit of mathematical problems offers
mental absorption,
peace of mind amid endless challenges,
repose in activity,
battle without conflict,
refuge from the goading urgency of contingent happenings,
and
the sort of beauty changeless mountains present to senses
tried by the present-day kaleidoscope of events."