"Because of the comparative simplicity with which mathematics can go beyond the superficial, it lends itself to the development of attitudes of lifelong and general value. To name but a few:
A healthy skepticism regarding accepted knowledge and a willingness to abandon ideas which are demonstrably erroneous.
The humility inherent in the realization that our understanding can never be complete, coupled with the optimism of conviction that, nevertheless, our understanding can always be increased.
The realization that understanding, while indeed a means to power, is a joy and an end in itself."
-Taken from The Goals of the Cambridge Conference on the Correlation of Elementary Science and Mathematics (1969).
"The interval [0,1] is a fish and you are a sushi chef "
"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together ina harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." -G. H. Hardy in A Mathematician's Apology