Poincare, Jules Henri (1854-1912)
The mind uses its faculty for creativity only when experience forces it to do so.
Poincare, Jules Henri (1854-1912)
Mathematical
discoveries, small
or great, are never
born of spontaneous
generation. They
always presuppose a
soil seeded with
preliminary
knowledge and well
prepared by labour,
both conscious and
subconscious.
Poincare, Jules Henri (1854-1912)
Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.
La Science et l'hypothese.
Poincare, Jules Henri (1854-1912)
...by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
Poisson, Simeon (1781-1840)
Life is good for only two things, discovering mathematics and teaching mathematics.
Mathematics Magazine, v. 64, no. 1, Feb. 1991.
Polya, George (1887-1985)
Mathematics consists
of proving the most
obvious thing in the
least obvious way.
In N. Rose
Mathematical Maxims
and Minims, Raleigh
NC:Rome Press Inc.,
1988.
Polya, George (1887-1985)
The traditional
mathematics
professor of the
popular legend is
absentminded. He
usually appears in
public with a lost
umbrella in each
hand. He prefers to
face the blackboard
and to turn his back
to the class. He
writes a, he says b,
he means c; but it
should be d. Some of
his sayings are
handed down from
generation to
generation.
"In
order to solve this
differential
equation you look at
it till a solution
occurs to you."
"This principle is
so perfectly general
that no particular
application of it is
possible."
"Geometry is the
science of correct
reasoning on
incorrect
figures."
"My
method to overcome a
difficulty is to go
round it."
"What is the
difference between
method and device? A
method is a device
which you used
twice."
How to Solve It.
Princeton: Princeton
University Press.
1945.
Polya, George (1887-1985)
Mathematics is the
cheapest science.
Unlike physics or
chemistry, it does
not require any
expensive equipment.
All one needs for
mathematics is a
pencil and paper.
D. J. Albers and G.
L. Alexanderson,
Mathematical People,
Boston: Birkhauser,
1985.
Polya, George (1887-1985)
There are many
questions which
fools can ask that
wise men cannot
answer.
In H. Eves Return to
Mathematical
Circles, Boston:
Prindle, Weber and
Schmidt, 1988.
Polya, George (1887-1985)
When introduced at
the wrong time or
place, good logic
may be the worst
enemy of good
teaching.
The American
Mathematical
Monthly, v. 100, no.
3.