by Giacomo on June 16th, 2008, 3:56 am
Learning
If I am given a formula and I am ignorant of its meaning, it cannot teach me anything,
but if I already know it what does the formula teach me?
– Saint Augustine of Hippo
So if man’s wit be wandering, let him study the mathematics: for in demonstrations,
if his wit be called away never so little, he must begin again.
– Sir Francis Bacon
Students attend our lectures, not because the mathematics we teach ‘makes lots
of fun’ for us, but because they believe they can learn some essential knowledge
from us. And each of our young students has only one life to live. We should
therefore be able to justify ourselves to our listeners with respect to what
we teach them.
– H. Behnke
To appreciate the living spirit rather than the dry bones of mathematics,
it is necessary to inspect the work of a master at first hand. Textbooks
and treatises are an unavoidable evil... The very crudities of the first
attack on a significant problem by a master are more illuminating than all
the pretty elegance of the standard texts which has been won at the cost
of perhaps centuries of finicky polishing.
– Eric Temple Bell
In Samoa, when elementary schools were first established, the natives developed
an absolute craze for arithmetical calculations. They laid aside their weapons and
were to be seen going about armed with slate and pencil, setting sums and problems
to one another and to European visitors. The Honourable Frederick Walpole declares
that his visit to the beautiful island was positively embittered by ceaseless
multiplication and division.
– T. Briffault
Thus metaphysics and mathematics are, among all the sciences that belong to reason,
those in which imagination has the greatest role.
– Jean D’Alembert
Whoever despises the high wisdom of mathematics nourishes himself on delusion.
– Leonardo da Vinci
Each problem that I solved became a rule which served afterwards to solve other problems.
– Rene Descartes
An educated mind is, as it were, composed of all the minds of preceding ages.
– Bernard de Fontenelle
The essence of mathematics is not to make simple things complicated,
but to make complicated things simple.
– S. Gudder
A good stack of examples, as large as possible, is indispensable for a thorough understanding
of any concept, and when I want to learn something new, I make it my first job to build one.
– Paul Richard Halmos
The value of a problem is not so much coming up with the answer as in the ideas and
attempted ideas it forces on the would be solver.
– Israel Nathan Herstein
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
– David Hilbert
The object of mathematics is the honor of the human spirit.
– Carl Jacobi
Everyone knows what a curve is, until he has studied enough mathematics to become confused
through the countless number of possible exceptions.
– Felix Klein
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.
– Morris Kline
The mathematician who pursues his studies without clear views of this matter,
must often have the uncomfortable feeling that his paper and pencil surpass
him in intelligence.
– Ernst Mach
I keep the subject constantly before me and wait till the first dawnings
open little by little into the full light.
– Sir Isaac Newton
A child[’s] ... first geometrical discoveries are topological ...
If you ask him to copy a square or a triangle, he draws a closed circle.
– Jean Piaget
There is no more a math mind, than there is a history or an English mind.
– Gloria Steinem
The study of mathematics is apt to commence in disappointment ...
we are told that by its aid the stars are weighed and the billion
of molecules in a drop of water are counted. Yet, like the ghost
of Hamlet’s father, this great science eludes the efforts of our
mental weapons to grasp it.
– Alfred North Whitehead