The mathematician has reached the highest rung on the ladder
of human thought.
Havelock Ellis, The dance of life
Behind these symbols lie the boldest, purest, coolest abstractions
mankind has ever made. No schoolman speculating on essences and
attributes ever approached anything like the abstractness of
Susanne K. Langer, Philosophy in a new key
[If] a proof convinces you that there is a root of an equation
(without giving you any idea where)---how do you know that
you understand the proposition that there is a root?
Ludwig Wittgenstein, Remarks on the foundations of mathematics
No one shall drive us out of the paradise which Cantor created
David Hilbert, On the infinite
I would say, "I wouldn't dream of trying to drive anyone out of this
paradise." I would try to do something quite different: I would try
to show you that it is not a paradise---so that you'll leave of your
own accord. I would say, "You're welcome to this; just look about
Ludwig Wittgenstein, Lectures on the foundations of mathematics
It was like a mathematical formula and no more difficult,
for mathematics was the one subject that had come easy to
Scarlett in her schooldays.
Margaret Mitchell, Gone with the wind
Quantum mechanics doesn't model the physical world, it reflects what
we can say about the world.
Robert Oerter, The theory of almost everything
The continuous function is the only workable and usable function. It
alone is subject to law and the laws of calculation. It is a loyal
subject of the mathematical kingdom. Other so-called or miscalled
functions are freaks, anarchists, disturbers of the peace, malformed
curiosities which one and all are of no use to anyone, least of all
to the loyal and burden-bearing subjects who by keeping the laws
maintain the kingdom and make its advance possible.
... scholarship lies in the direction of paying deference to the loyal
continuous function rather than to the outlaws of mathematical society.
E. D. Roe, Jr. A generalized definition of limit, Math. Teacher
If one is interested in the relations between fields which, according
to customary academic divisions, belong to different departments, then
he will not be welcomed as a builder of bridges, as he might have
expected, but will rather be regarded by both sides as an outsider
and troublesome intruder.
Rudolf Carnap, Intellectual autobiography
Education has become a prisoner of contemporaneity. It is the great
past, not the dizzy present, that is the best door to the
Camille Paglia, Sex, Art, and American Culture
When I spoke to Maxim Brazhnikov, the only Soviet scholar
specializing exclusively in old church notation, he said
not without bitterness, "You probably think that my list
of publications is small. Yes, it is. But at home I have
stacks of unpublished manuscripts which I cannot get into
print; some are accepted for publication, but there are
interminable delays. And there is no serious student
interested in my field, I have no one to whom I could
pass on my knowledge..."
In his efforts to decipher the old church notation,
Brazhnikov worked out a statistical approach which, he
said, aroused "derision". "I know more about these things
than anyone else ... but no one wants to learn ...
everything is directed towards contemporaneousness."
He was indeed a pathetic figure---a scholar of immense
erudition, caught in an environment of total
estrangement and indifference.
Boris Schwartz, Music and Musical Life in Soviet Russia
But a machine that was powerful enough to accelerate particles
to the grand unification energy would have to be as big as the
Solar System---and would be unlikely to be funded in the present
Stephen Hawking, A brief history of time
One man's modus ponens is another man's modus tollens.
Neil Tennant, Philosophia Mathematica, February 1998
Perhaps the greatest educational fallacy is the notion that a person
learns only what he is studying at the time. Collateral learning
in the way of formation of enduring attitudes ... may be and often
is more important than the spelling lesson or lesson in geography
or history ... For these attitudes are fundamentally what count in
John Dewey, Experience and education p. 48
Last modified September 3, 2006