To Thales the primary question was not what do we know, but how do we
know it. ---Aristotle
It is not once nor twice but times without number that the same ideas make their appearance in the world. ---Aristotle
It appears to me that if one wishes to make progress in mathematics,
one should study the masters and not the pupils. ---Niels Abel
The joy of suddenly learning a former secret and the joy of suddenly
discovering a hitherto unknown truth are the same to me -- both have the
flash of enlightenment, the almost incredibly enhanced vision, and the
ecstasy and euphoria of released tension. --Paul Halmos (I want to be a
Every mathematician worthy of the name has experienced ... the state
of lucid exaltation in which one thought succeeds another as if
miraculously... this feeling may last for hours at a time, even for days.
Once you have experienced it, you are eager to repeat it but unable to do
it at will, unless perhaps by dogged work... --André Weil (The
Apprenticeship of a Mathematician).
Don't just read it; fight it! Ask your own questions, look for your
own examples, discover your own proofs. Is the hypothesis necessary? Is the
converse true? What happens in the classical special case? What about the
degenerate cases? Where does the proof use the hypothesis? --Paul Halmos
(I want to be a Mathematician)
Since the mathematicians have invaded the theory of relativity, I do
not understand it myself anymore. --Albert Einstein (Quoted in P A
Schilpp, Albert Einstein, Philosopher-Scientist (Evanston 1949)).
But the creative principle resides in mathematics. In a certain
sense, therefore, I hold true that pure thought can grasp
reality, as the ancients dreamed. --Albert Einstein
Everything that is really great and inspiring is created by the
individual who can labor in freedom. --Albert Einstein
Most of the fundamental ideas of science are essentially simple,
and may, as a rule, be expressed in a language comprehensible to everyone.
Great spirits have always encountered violent opposition from
mediocre minds. --Albert Einstein
Why are numbers beautiful? It's like asking why is Beethoven's Ninth
Symphony beautiful. If you don't see why, someone can't tell you.
We have a habit in writing articles published in scientific journals
to make the work as finished as possible, to cover up all the tracks, to
not worry about the blind alleys or describe how you had the wrong idea
first, and so on. So there isn't any place to publish, in a dignified
manner, what you actually did in order to get to do the work.
--Richard Feynman (Nobel Lecture)
To those who do not know mathematics it is difficult to get across a
real feeling as to the beauty, the deepest beauty, of nature ... If you
want to learn about nature, to appreciate nature, it is necessary to
understand the language that she speaks in. --Richard Feynman (The Character
of Physical Law)
... the two operations of our understanding, intuition and deduction,
on which alone we have said we must rely in the acquisition of knowledge.
Genius is what makes us forget the master's talent. --Ludwig
Any good idea can be stated in fifty words or less. --Stan Ulam
Take chances, make mistakes, get messy!-- Ms Frizzle in Magic School Bus
The most important outcome of education is to help students
become independent of formal education. ---Technology Review
When you build it, he will come. --- from Film "Field of Dream"
More things grow in the garden than the gardener grows. ---Spanish
To conceive is a pleasure. ---Gauss
But to give birth is painful. ---Poincare
When you look at the history of technology, you see that the principal
applications do not evlove incrementally, but are created by the technology.
Until you come up with such applications, you cannot judge how promising
technology is. It is foolish to ask immediately what a new technology is
good for. ---Herbert Kroemer, Winner of 2000 Nobel Prize in Physics
Don't worry about people stealing your ideas. If your ideas are any
good, you'll have to ram them down people's throats. ---Howard Aiken