"A common experience, when some colleague would try to explain some piece of mathematics to me, would be that I should listen attentively, but almost totally uncomprehending of the logical connections between one set of words and the next. However, some guessed image would form in my mind as to the ideas that he was trying to convey-formed entirely on my own terms and seemingly with very little connection with the mental images that had been the basis of my colleague's own understanding-and I would reply. Rather to my astonishment, my own remarks would usually be accepted as appropriate, and the conversation would proceed to and fro in this way. It would be clear, at the end of it, that some genuine and positive communication had taken place. Yet the actual sentences that each one of us would utter seemed only very infrequently to be actually understood!" (Roger Penrose, The emperor's new mind)

"With the formulation of analytical geometry and the theory of algebraic functions, with the development by Newton and Leibniz of calculus, mathematics ceases to be a dependent notation, an instru¬ment of the empirical. It becomes a fantastically rich, complex, and dynamic language. And the history of that language is one of progressive untranslatability."(George Steiner, The retreat from the word)

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