THe skilful Nymph reviews her Force with Care;

Let Spades be Trumps! she said, and Trumps they were.

Alexander Pope, *The rape of the lock*

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 algebra.

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

Ludwig Wittgenstein, *Remarks on the foundations of mathematics*

No one shall drive us out of the paradise which Cantor created for us.

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 you."

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

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
**3**(1910) p.47

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 future.

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 economic climate.

Stephen Hawking, *A brief history of time*

One man's

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 the future.

John Dewey, *Experience and education* p. 48

Last modified September 3, 2006